When I became Catholic I knew only a few Catholic people so my godmother was a sort of default pick. I have since come to find that she is one of the worst people I have ever and will ever know and she has even threatened to kill me and steal my dog.
I think once chosen, that’s it, but you could informally just pick someone else to replace her.
It’s sort of like with our families. We don’t always get along with them, and later, we can find friends who are more “family” than “family”.
My sister is far away from family, and we’re not a close-knit family, anyway. She said she took it upon herself to invite people to be her family. She would go up to someone and ask her to be, say, a sister to her.
So, I can´t see why you can´t go up to someone and ask someone else to be your godmother. I would not try to “fire” your existing godmother, just find a replacement.
It doesn´t work out much of the time picking godparents, anyway, because a lot of people long since fall away from the faith and more. I don´t even really know my godparents, would never have expected anything from them even if I did. I think, one, or possibly both, left the faith.
I have no idea where they are, if they are alive or not.
