You don't adopt children of your own familial bloodline, so that answer doesn't really make sense to me. Perhaps by not giving tom the Corleone name it's more of a way to keep him outside the "line of succession" as it were since leadership in the GF universe seems to pass through hereditary lines. Maybe it was seen as legitimizing tom and thus making his German/Irish ethnicity less important. The Corleone name is a "big deal" and invokes a response from all those concerned.

I know this is a bit of a stretch, just letting my mind wander wink