You really cannot go wrong with simply "pet".
During playtime, every vile, degrading phrase I can think of comes out. But then again, I probably lack maturity :P
Pet is a nice generic term of endearment which happens to have some D/s signifigance.
Lets see, I'll shit out a nice little acronym for it:
Painfully Extended Tenure? no, needs context
Pet Eats Tar? hrm, definately no.
People Earn This? actually, I like that a lot, being that it is a name and all. Would work well for a sub who enjoyed humiliation... "PEOPLE have names, dear pet. Maybe one day a little *insert derogatory term* like you can have one too!" mmm
Pussy Endures Training? Hrm, sounds forced and vulgar, but I do like it.
Pet Enduring Training... we have a winner! if anyone ever askes me what 'pet' means, after I beat them in the head with an obvious stick, this is the acronym I will give.... yes.
For me, its just a nice way to affirm position in the relationship.
Also, i've come to find out that the southern 'darlin' has possessive connotations to some people. I'm southern, I call the teller at the super market darling.... *shrug*