I looked into a lot about David because that was my late dad’s name and we used it as a middle name for my son. Dave, Davis, Davey/Davie, Daven are more well known variants. Dawson means son of David, but that doesn’t really work since it’s your brother. I’d pick Daven or Davan if I were you because it sounds like David and Brendan combined. Or you could honor them by having the same name meaning. David means beloved/dear and Brendan means prince or chieftain. Just google those meanings unless you want me to give you some just let me know.
That’s my son’s name, David, very nice name
Maybe Daren? (Darren)
Daveon
Dayan