Take the advice of many, many women I have read about on here and DON'T give the baby his surname. Put his surname in with the middle names, yes. BUT DON'T DON'T DON'T give his name as a surname.
There are lots of good reasons for this.
If the baby has his surname, you can't change it without his permission. You might think you don't want to... But what if, three years down the line, he and his mother are giving you hell, plus you've met a lovely guy, are planning to get married, and you're expecting another baby? You could end up with a family where you all have one surname apart from your first baby. Nothing you could do about it.
They could also use the surname issue to cause problems for you. It's a great way to control you - if the baby has a different surname to you, you will have to carry a letter with permission to go abroad from your ex. Schools, doctors...everything official will be connected with his name. It may really, really end up not being what you want. But once his name is there, thats it. You can't change it without his say-so.
If you give the baby YOUR surname, control stays with you. And if, three years down the line, you and he are getting on well, co parenting, and his mother knows not to mess with you and is being supportive, you could choose to add your ex's surname then. Or, your child could make that decision when older.
But mainly, give the baby your surname because as a single mother, it will be YOU doing the work. You living with the baby, registering with schools and doctors. Your child may end up not even seeing this man, but will be stuck having a different name to his/her mum.
You are going to be the family your baby knows and lives with. Give him/her the security of having the same name as you.