I have a few power animals.
The first one I ever "met" was the black panther/jaguar. I found him (I always refer to it as a "Him") through a shaman, who lead me in meditation to find my power animal. When I met him, he never gave me a name to call him, so I always refer to him as "black panther". However, I have often "felt" him with me--and I mean literally "felt" him. I can feel his fur at times--when he is standing right next to me!
I have connected with him mostly in meditation and astral traveling. The funny thing is he has also shown up for other people reading me--in their readings. Some were quite surprised to have a black panther come to them!
I also have the Tiger as a power animal, and other animals I have had come to me many times were the crow/raven (I can't be sure which it is), an eagle, and a horse! The Tiger also came as a result of a shamanic meditation that I did. I also had a hummingbird for awhile--as I am not sure the hummingbird is a power animal that is staying with me. It has shown up a few times--and again, has also shown itself to a psychic reader I went to for a reading. That reader also picked up on the panther and also saw the phoenix for me--but I have never connected to the phoenix myself that I can recall. The phoenix did have a message for me delivered through that psychic--and I can't recall what it was now--but when I was told it, it made perfect sense to me then.
Some power animals will only be with you for a short time--as they are here to help you with something- a lesson perhaps and then when that is over, they can leave you. But I do know that the black panther is with me for the rest of my life and I think the crow/raven probably is too. I also feel red tail hawks are a power animal for me as I see them often in my meditations too--as well as in real life.
If I know that I need guidance or help in a particular area, I may call on a specific power animal to be with me and to guide me on the right path. Or, I sometimes just luck out and the right one comes when needed. Sometimes I have not asked for any help/guidance and then in my meditation--they appear to me. Sometimes when I'm doing a psychic reading for another person/doing my spirit work--(calling on the deceased)--or whatever.
Are you interested in finding yours, is this the reason you are asking these questions?