Am I Suppose To Give My Son His Last Name?

I currently found out I was 05 mnths pregnant about a few weeks ago. I didnt know i was pregnant till up till recently (was showing no symptoms). I tld the father of the bby and he kept telling me that he was "not ready" and wanted me to get an abortion. I schedule a doc appt ignoring the abortion comment and they set my due date to July 22, 2017. I tld him tht i heard the baby heart beat and everything. He kept telling me he wasnt ready and then stopped replying to my texts and answering my calls. Tht was almost a week ago. He also has another child by another woman. I deleted him off my social media accounts been trying to get over the hurt tht I have but my friend thinks I shuld give my son his last name and I think he dnt deserve it at all. Am I just being tht "spiteful baby mama" cause i refuse to give my child his last name?