In the movie Star Trek: The Motion Picture they show or imply why/how V'Ger was named, however, this is confusing and makes no sense. Why would a computer call itself something based on the name "Voyager" being smudged on it's outer shell with some sort of soot? A computer would know it's own name from it's programming.
Memory Alpha explains that:
The center contained the oldest part of V'ger – Voyager 6, an unmanned space probe launched by NASA in the late 20th century. The entire vessel surrounding the Voyager probe was built by an unknown race of machine entities in order to help it complete what the latter interpreted to be its primary programming: "learn all that is learnable," and return that knowledge to its creator. During its journey, the probe came to think of itself as V'ger after the only remaining legible letters from its original name (the "O", "Y", "A" and "6" on the nameplate being obscured from encounters with previous spatial hazards) and amassed knowledge to such a degree as to become self-aware.
Although the bolded part of the quote is the most important, I've included the whole paragraph to highlight the fact that V'Ger was encountered by an alien race. The alien race probably encountered V'Ger when the O, Y, A and 6 had been obscured, so told it that its name was "V'Ger". Remember that V'Ger hadn't developed a state of self-awareness initially, so it probably was given that name by the alien race.
The big question is how the machine planet aliens learned how to read and pronounce English.
Obviously Voyager 6 could have carried some visual and audio records which enabled the machine planet super duper ultra hyper computers to figure out to read and speak English. But apparently there were some gaps in the records due to space hazards which just happened to include the name of the space probe so the the only clue the machine planet people had about the name was the already partially illegible nameplate on Voyager 6.
V'ger's ignorance of its true name of Voyager 6 was necessary for the plot because if it said it was Voyager 6 they would search the records for the communications codes and other useful data. But it required some really convenient selective damage to Voyager 6's records and nameplate.