Should I change my sons last name?

My sons father hasn’t seen him since he was 4 months old, he’s now 2 1/2. After multiple attempts to have his dad see him, I’ve given up. When he was born I gave him his last name. He’s now in a pre school program and im thinking of changing his last name but don’t want my son to be upset with me when he grows up, but also don’t know if I should put him through school learning a last name of a man he hasn’t seen more then 10x in his lifetime…