The One With All The Haste - S4-E19
Factual error: The guys are gone for a single night, watching the Knicks game. (You can tell this because they talk about how "we can go see the game tonight," and when they get back everyone's wearing the same clothes as that conversation.) When they get back, both apartments are completely switched back: the large, heavy furniture is replaced, the posters are re-hung, etc. Even if they were gone from, say, 6 p.m. to midnight or so, there is no way that Rachel and Monica would be able to make that transition in that kind of time.
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.