Oli, the nominal reason is found in the novel: Vito insisted that Tom honor his father's memory by never forgetting who he was, even though his father was an abusive drunk.

BUT: we can read a lot more into it--did Tom really think he wasn't accepted as a full-fledged family member? (after the Tahoe attack, he practically bawls with gratitude when he tells Michael, "I always wanted to be regarded as a brother by you"). Or did Vito, ever calculating, want his future consigliere to retain his non-Italian name--the better to be accepted by the largely Irish and Jewish politicians and judges Vito needed?