What if I told you I wanted to call him daddy or at least big bro?
For real? What made you want to call him that?
Cause he's obviously the biological father
Communication is a key part of a relationship, so sit down and talk to them and find out what they are comfortable with being called. It's better to make them feel welcomed than to feel weird.
I'm not a child, I can communicate just fine.
If it makes someone uncomfortable then you should not do it. Communicate with gentle and caring words. This is something that will come back to you in a good way as well.