In real life I've purchased and adopted animals.
When I get them home, I can name them whatever I want, regardless of what the previous people called the animal. An exception to this is registered horses and livestock, but even with them you can call the animal whatever you want, they just have an official name for the bloodlines.
Why not have pets in Lineage][ able to be renamed?
I was thinking of this in light of the recent hatchling changes, where previously-tankable breeds are no longer tankable, which might motivate some to trade their current breed with something more suited for their class.