How does V'ger even know its name? I suppose you could argue that once it zaps Ilia it has access to her memory and can then recognize the letters on its nameplate. Upon realizing these marks mean something, you'd think the first thing it would do is scan the holy fuck out of that nameplate for more information. It is rather a logic problem that the writers didn't consider.
TWOK hangs on a dozen too-convenient coincidences, including: Reliant can't tell one planet from another, Ceti Eels only make victims susceptible to the bad guy's suggestion, Kirk just happens to be on the Enterprise when normally he isn't, Genesis is a Manhattan Project in space with zip security, Enterprise can detect Reliant on the opposite side of Regula but not vice-versa, and when Genesis blows up in a nebula instead of on a planet as designed, it miraculously sucks all the nebula material into a planet which just conveniently happens to be in the Goldilocks zone around a convenient star.
Plot Hole-ier than thou.