The Barg Surname
Family names are a relatively modern concept. Among non aristocratic European Gentiles, surnames began appearing in the eleventh century, but became obligatory only towards the 19th century: in Austria in 1787,  in Frankfurt on Main in 1807, in French occupied Rhineland and Westphalia in 1808, in Baden in 1809, in Prussia in 1812, in Bavaria in 1813, in Prussian occupied Posen in 1833 and in Saxonia in 1834. Polish surnames had been known since the Middle Ages, but only after Napoleon Invasion they become compulsory (Jews in Podolia had to registrate a surname in 1804). The last Europeans to adopt the "two name" pattern were the Scandinavians and permanent surnames became compulsory by law in Norway only in 1925.
The acquisition of surnames has been affected by many factors, including social class and structure, cultural tradition, and naming practices in neighboring cultures. Prior to the use of them people lived in small communities and had little need of distinction beyond their given names. When more than one person lived in such a small community they were usually differentiated by their patronymics (e.g. Avner ben Ner, Chief of Staff for King Saul's army), their trade (Taylor, Smith, Baker), a distinctive feature (Essau the Red Headed, Goliath the Giant) or the locality in which they resided (Naboth the Jezreelite, Jesus the Nazarene). Jews in Eastern Europe were among the last ethnic groups to acquire surnames due to their reluctance to take part in censuses, tax collecting, and conscription. Therefore for centuries Jews were known by the traditional "Torah name" by which they were called to the pulpit on Shabat and this was made by their Given name + patronymic + tribal belonging (Cohen or Levy) unless they had a very prominent status in the community or the religious life in which case the title was added.

BARG is both the Yiddish and the Low German word for Mountain, as opposed to the High German pronunciation of BERG. As a surname it is not common, with a popularity rank of 44619 in the U.S.A. It appears more often as part of complex surnames (Weissbarg=White Mountain, Silberberg=Silver Hills) than as a solitary name. Among Jews, according to the erudite works by Alexander Beider, the principal regions of Europe were it used to be relatively common were the Gubernias of Podolia and Kherson in the Russian Empire. By the Daitch-Mokotoff Soundex System it receives the same code as BERG, BURG and BORG, forms with a harsh consonant instead of the "G" like BARCH, BARC, BARK, BARCK, BERCK and two syllable variations like BAROK, BARUCH, BEIRAK, BORAK, BARAK, BORUCH, etc.
Not all the Bargs/Bergs of the World are related among themselves and some have inherited the name from one source while others from a completely different one. Some Bargs changed their names to adapt it to their country of residence and have become Bergs, Barks, Barcks, Baraks, etc. while others who had a longer or complex surname decided to adopt a shorter version and became Barg (a case I know of is somebody named Weisenbarger). Surname spelling and pronunciation has evolved over centuries, with our current generation often unaware of the origin and evolution of their surnames. Among the humbler classes of European society, and especially among the illiterate, individuals had little choice but to accept the mistakes of officials, clerks, and priests who officially bestowed upon them new versions of their surnames, just as they had meekly accepted the surnames which they were born with. According to a verbal tradition, for example, a branch of our family became BARK due to an official and accidental change caused by a Czarist clerk during a 19th century census.

Broadly, most surnames fall into four categories.
  • Geographical, locational or topographic surnames, derived from the place where the bearer lived.
  • Surnames derived from Patronymics & Matronymics.
  • Occupational surnames refering to the occupation of the bearer.
  • Surnames derived from Nicknames and Descriptive - based on a unique quality or physical feature of the individual.
Based on this classification here are some theories regarding our name:

Geographical Origins for the Surname Barg

As already mentioned, BARG is the Yiddish German word for Mountain and a probable origin for the name is an allusion to mountains in general or to a specific one, even one of the two special "Mountains" in Judaism: Mt Sinai were the Ten Commandments were given and Mt Moriah, were the Temple stood in Jerusalem.
Thus Barg could be a topographic name for someone who lived on a hill. Another possibility is that the surname could describe the origin of an individual as somebody coming from a place called Barg or Berg and indeed such places exist: the town of BARG is situated in the coordinates 5444 941 in Jutland, Germany, 215.8
miles NW of Berlin and there are 122 towns named BERG in Germany, Austria and the Czech Republic. Another possible source, mentioned in the Database of the Museum of Diaspora, is the former German Duchy of BERG, nowadays incorporated in the administrative districts of Dusseldorf and Cologne. And finally there is a theory we are actually Sephardic Jews and our origins are in the town of Bargas, near Toledo in Spain or in Italy, either the city of Bari, Bergamo or Barga in the province of Lucca, Toscana. Another way of getting a surname connected with Geography was when Jews lived in the vicinity or under the auspices or in lands belonging to a Gentile, the most famous example being the Jewish Gordons of Lithuania who probably got their surname living being serfs under Patrick Gordon (1635-1699), a mercenary in the Polish-Swedish War who became a favorite of Tsar Peter I the Great and got from him lands, the title of rear admiral and became his chief military counselor. In the Ukraine there were many Gentiles named Barg, of the Mennonite Persuation, who were prominent farmers. There is a possibility that some Jewish Barg ancestors got their surname for having lived near or in the lands of a Mennonite Barg in nowadays Ukraine.

Patronymic & Matronymic Surnames
Among Jews patronymics were sometimes given in a oversimplified form, the father's name becaming the surname as it is: Moishe Salomon is actually Moishe son of Salomon and thus Barg could be a mispronunciation of Baruch (Borech in Ashkenazi Yiddish accent). The first famous Baruchin history is "Baruch the Scribe son of Neriah" mentioned in the Book of Jeremiah [Jeremiah 36:26] and regarded by many scholars as one of the authors/editors of the Bible. Baruch means "The Blessed" and interesting enough in the Barg family there are several Baruchs, Ashers/Ushers (another hebrew word meaning Blessed) and Zelig/Zelik, the Yidisch Ashkenazi KINUI (Hebrew for alias, being actually the Legal/Hebrew Given Name or the name by which a person is known) for both Asher and Baruch.
Another peculiar patronymic among Jews, unique to families holding surnames beginning with the letters BAR, BER, BR and other diminutive forms is the acronym "Ben Rabbi" or "Bar Rabbi" (son of the Rabbi). According to the Museum of Diaspora computerized data and a familiar tradition, BARG might have been originally an acronym formed by the first letters of Ben Rabeinu Gershon or Gershom (son of our Rabbi Gershon or Gershom). This is very interesting since several branches of the family have many male members named Gershon or Gershom. Who could this Rabbi Gershon be?
We would like to think it refers to Rabeinu Gershom bar Yehuda (HARAGMA) "The Light of the Diaspora", the most famous and important Rabbinical Figure in the Middle Ages. The main problem with this hypothesis is that the only male descendant to the RAGMA we know about (his son) forsook his religion at the time of the expulsion of the Jews from Mayence in 1012, converted to Christianity and died during his father's life (actually Rabbeinu Gershom grieved for him, observing all the forms of Jewish mourning, in spite of his conversion, and his example became a rule for others in similar cases). Although it is known that a daughter survived him, no direct genealogical link to her has been found.
Could this Gershon be the noted French Torah commentator and mathematician Gershonides, or Rabbi Levi ben Gershon (known also as the RALBAG)?. In the 17th century, some Jewish families were using family names approximately as we use them today, most frequently as a way of mentioning their relationships with prominent ancestors and many descendants of Gershonides used a similar family name to call attention to their ancestry. The surname RALBAG actually exists till today and there is even a Rabbinical family by that name (Rabbi Jehoseph H. Ralbag and his son Rabbi Aryeh Ralbag.
Could the Gershon we are looking for be Rabbi Gershon Ashkenazi or Rabbi Abraham Gershon Kitover, brother in law of the Baal Shem Tov (the Kitovers were a prominent Rabbinical family and we do have a Rabbi Asher Zelig Barg among our ancestors who lived in the vicinity of were Reb Gershon lived. This could also explained the BARG-BARK variation Ben Rabbi Gershon Kitover?). Another candidate is Rabbi Gershon of Lotzk, a student of the Baal Shem Tov, who died in 1745 (-1788?) without dinasty. As tempting as they are, all these hypothetical ancestries looked to me a little far fetched and my personal view is that if a Gershon is connected he was probably of a much lesser known family.

Occupational Surnames
The only occupation related to our surname is sailing. Barge is a flat-bottomed boat, built mainly for river and canal transport of heavy goods (from Old French barge, from Vulgar Latin barga). The word originally could refer to any small boat and so did Bark ("small ship") which comes from Old French barque, from Vulgar Latin barca, both probably derived from Latin barica, Greek baris ("Egyptian boat") and ultimately from Coptic bari "small boat."

Descriptive Surnames - Based on a unique quality or physical feature of the individual
Among the most common forms of surname found are those that are derived from nicknames. Nickname surnames were derived from an "eke-name" or added name. They usually reflected the physical characteristics or attributes of the first person that used the name. I am 6'4'' and many Bargs were known to be of substantial height. Could our surname be a nickname for tall individuals? After all, this is the reason famous NBA player William "Bill" Walton is known as "Mountain Bill".