I use 5 pets out and I always hide them cause I find them distracting or simply I don't like the aspect, but I wouldn't mind to see some of them.

This could be done adding an option to show/hide a specific pet in the pet window. So you can have 5 out, but show only 2 for example. Another option I would like to have is show/hide all pet names.

Sounds like a good idea. I would also like an option to show/hide all birds(or all flying pets), because I find birds/flying pets distracting during combat, but pets that stay on the ground usually don't bother me.