In "The One With The Fake Monica", a woman (referred to as the Fake Monica) steals Monica's credit cards. Monica becomes obsessed with the fact that the Fake Monica is living her life and doing it better than her. She goes to a tap class that the Fake Monica is enrolled in, and winds up meeting and building a friendship with her.
Eventually, the Fake Monica is arrested for stealing the credit card, and Monica visits her in jail to thank her for giving her the experiences she gave her.
Her real name is never reveled.