There is a limit of 5 players taming the same pet. Once it reaches 5 it says:
"This animal has had too many owners"
For each new owner the taming difficulty goes up. In some cases the 3rd owner breaches the 120 mark and makes the pet untamable even for a legendary tamer. This infact increases the command difficulty as well so beware!
Transferring (selling) a pet avoids this difficulty raising.
What I do is at the jehelom farms ill tame with the 1st tamer, the one with the lower skill, rename then tame with my 2nd tamer, higher skill, rename release.
Sometimes there another player there, other times I release a drake outside the pen to slowly knock off the previously tamed. I use the drake because it give the 2nd tamer plenty of time to gain from it.