I don't think you are nuts at all. Your reason behind wanting to change your name a valid and make sense, at least to me. I was also raised by a narcissistic parent and wish I could get away. Right now, that is not possible, tho.

People would get used to the new name eventually, but there would always be the ones that call you your original name.

You could start by just introducing yourself with the new name when you meet people and start asking close friends to use it, even before legally changing it. That way you can also get a feel for if the name you pick is right for you. Maybe even try out a few names with those thatf are really close just to see if you like how they sound...

I think if you feel you need to change your name, to truly heal from the way your father was, then you should absolutely do it. Other people's opinions don't matter. It's what you need.