Different last names

We're all gonna do what we're gonna do but it makes me really sad when I see unmarried, not even engaged, couples giving their child the father's last name. Hear me out though- it's not because I'm old fashioned or stuck up, it's because I did that and really believed I was doing the right thing. To cut a very long story short, I was blinded by love and stuck to a guy who wouldn't even consider being engaged but was extremely controlling. We have our son his last name because "we'd get married ONE day!" And "it's the right thing to do."
Well, that boy is now 10 and for the last 6 years he's been raised by my husband (not his father). His father decided he hated me and the baby and just said screw it when he was almost 3. My son knows his dad and sees him on occasion and doesn't care for him. The last name issue upsets my son because now he's the only one in a family of 6 with a different last name. BEFORE PEOPLE TRY TO ADVISE ME ON HOW TO CHANGE MY CHILDS NAME I WILL GET TO THE POINT: it's really hard to change a child's last name without consent from both parents. So, it's much easier to give the child the mother's last name and change it to the father's if you get married.
Example: if Mary Smith and James Jones have a baby and name it Sarah Smith, if they get married they can both consent to change her name it Sarah Jones. If they don't get married and James decides he'd rather hook up with random women and snort coke, no big deal- Sarah doesn't have to grow up resentful of her last name!
But, if Mary Smith and James Jones name their baby Sarah Jones but James Jones runs off before buying a ring for Mary, Sarah is basically stuck as a Jones until she can change it herself or James says it's okay to change it.
So, glow, tell me why I'm wrong 😂

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