I've seen multiple ways to finding out theriotype names, but I was just randomly thinking one day nd decided to try my own way.
for my horse theriotype(I haven't tried it for my falcon theriotype yet) I just searched horse names. I looked through lists in multiple websites and found a name I was strongly drawn to, Azalea. For a little while I thought that was her name, until I felt like I was supposed to search some more, so I did, and found a website that had a few Native American names and finally found Niabi. I made sure Niabi was her name this time through meditation.
I would recommend trying this, but like the paper and pencil method, isn't 100% accurate.