So you want a name that is share with many people in your family? So why not just pick a name from among your family members' names and go with that?
If you don't like
Tom or
Tommy, politely ask people not to call you either of those. My name is
Catherine, and I've corrected people when they're called me
Cathy or
Katie.
You are confusing, because in the OP you specifically said you hate your name because your FN and LN start with the same 3 letters and they are thus too close. Not you're giving completely different reasons.