My BO has a horse who had a really rough past, so she renamed him to open up for a whole new life, a better one. He used to be "Lats" (same as "Dollar" in English), and now he is "Naudins" ("Coin" or "Money"). As everything has gone only uphill for this horse, I don't really believe it is bad luck to rename a horse. :)
And a horse who belongs to a friend used to be Raritet, but his name was changed to Radi, and he's been only happier and calmer since he's with my friend.
I have also renamed my cats I got from rescue - Dana became Arthemis, Blacky became Ayeed and Greeneyes became Nimue, and also my dog, Dwarf (he was the smallest puppy of the litter and the owner believed he'd turn out unhealthy and smallish, wich didn't turn out to be true - he was beautiful and healthy all his life :) ) - well, he became Haiko. And all for the best of their luck.