Strange coincidence
I don’t know very much about charr lore, but i was a bit surprised too when i did that part of the story. However, i think it kinda makes sense that if a charr’s father is an honorless gladium, the charr would change his own name, or as a cub not be named after his father at all.
But if you do want to change your name, i think an item can be bought for gem that lets you change it.:)