I have a pen and I put in there a tamed lizard doggo. It stayed there until I wondered out of render distance, then it despawned.
After that I tamed 3 more, put in the pen, and when I went out of render distance they despawned as well.
They stay in the pen unless I wonder too far away. At the moment there is no point to tame them.
I am playing Stable Update #2 101873