The way the bones import (visually) is actually not that important as long as their transforms are correct, which normally it should be. I understand you want to see nice clean skeleton, but the best thing is to just leave them alone, as imported.
What I actually do for import, is to use dummies in stead on the import setting, in which case each bone is represented by basically a small box, which is much cleaner looking. Then you can build a rig on top of that.
Personally, for a custom rig, I’d keep the imported bones as is, then build a new skeleton on top as the control rig, and hook up the imported bones to follow. This way you keep your “game skeleton” clean and separate, and you know that it will export and work 100%. It’s pretty much always better to work with a control rig separately, regardless of using imported skeleton or not, just because when you create the rig, you may want to do things to the bones that could influence how things export, or even have a different hierarchy, so keeping them separated is the safe way to work and frees you up to do what ever you want with the rig and not worry about breaking the base skeleton in some way.