The One In Massapequa - S8-E18
Character mistake: In the early years, the gang are talking about their pets dying and their parents saying they sent them to a farm and Ross thinks that actually exists. He said that they sent their dog Chee Chee there and HE could run about chasing animals. Then in TOI Massapequa, Monica is preparing her speech and she tells Chandler about Chee Chee and said SHE died when Monica was in school, and when Parker asks whose dog it is, Monica says HE's my old dog. Then during her speech, Monica says HER and Nana are gone. (00:15:30)
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.