In Friends, I have noticed that Phoebe most of the time uses the same fake name: Regina Phalange. Is this random or has a story or some hidden meaning?
It is her alter ego that she uses, often when she needs to get herself or one of her friends out of a jam. Here's a brief description:
Phoebe frequently uses the alter ego Regina Phalange. Once when she is pretending to be French, she even adopts a French version called "Régine Filange". The first reference to Regina Phalange is when she is trying to contact Mrs. Waltham in England at Ross and Emily's wedding, and pretends to be a Dr. Regina Phalange who is Ross's brain doctor, she tries to justify Ross's hiccup when he said Rachel instead of Emily at the wedding it was due to his not taking medication and thus names are interchangeable in the mind of Ross, when Mrs. Waltham discovers that it is Phoebe, she remarks she has the illness too! The last reference is in the series finale when Phoebe successfully stalls Rachel's plane to Paris by saying there was a problem with the "Left Phalange." (wiki)
To determine why she uses that name, lets take a look at when she uses that name.
According to this wiki page:
The first reference to Regina Phalange is during season 5 following Ross saying "Rachel" instead of "Emily" at his wedding.
By this point, she already contracted the house maid, but couldn't speak to anyone useful. She adopts the name to get around anyone who maybe suspicious, the maid could have warned certain family members not to talk to Phoebe.
Another occurrence, is when they're all in Vegas and pretends to be an executive at a firm, she helps Joey with the hand twin plan only to be thrown out again.
The show doesn't say when Phoebe decided to start using the name, from what we can gather, she was at one point homeless and didn't really know where or what she wanted to do with herself. Given the above link, we can assume she adopted the name for the same reason one might use a pseudonym, to avoid being caught or to use it for sketchy purposes where she doesn't want real information being given out. She was at one time a thief (she mugged Ross), and confirmed by Gary (the cop who shot a bird), she has a police record. She also uses it when her real name has been associated with events or people that aren't exactly legal. Having a police record with the name Phoebe Buffay can sometimes complicate the most trivial interactions in daily life, so for her it helps to have a fake name.
Given that the person doesn't exist, she can make up an occupation, or any background facts on the spot, where as Phoebe is masseuse, with a home address, and friends that know her.