You've been thinking about it quite a bit. I see no reason not to do it if you want to. My cousin's sons all from the same father have different surnames.

Son 1's surname = father's surname-mother's surname
Son 2's surname = father's surname
Son 3's surname = maternal grandmother's maiden name

Son 3 had a similar relationship with his father as you described and had always felt closer to his mother's (and my) side of the family. So he changed his name. Since then, he and his father have improved their relationship. But he likes his name.

Genealogically, it looks funny, but each individual is happy with his choice.