I only name my selfbows if they inspire me while being crafted and shooting them in. I have named four of them, all Osage:
Vlad (my wife named that one) the first selfbow I took an animal with.
Max, a sweet shooting bow that reminded me of my old yellow lab. Neither were much for hunting but you just had to love the old love pigs.
Budster (the bow I took my kitty with), named after my black lab that was nine years old, but acted like he was still six months old, neither ever learned to take/make it easy.
Last is Pigger, named after my chocolate lab. A little slower on the hunt, but steady, true, and reliable; she always got the job done until time took its toll.