You won't be the first, nor the last that this happens to. It's truly shitty.
Honestly, I'd give him an ultimatum. He has until the end of the year to propose or you're leaving (or similar). I highly doubt you would have had kids with the man if you knew his true intentions and it's totally unfair you've upheld your end of the bargain, so to speak, but he hasn't upheld his.
Or, you could call his bluff. If it's only a piece of paper then he'll have no issue going to the registry office next weekend, will he? See his reaction. If he wants to marry you but he's just lazy he'll be down for it. If he doesn't want to marry you, you'll know by your reaction.
Ultimately, there's nothing wrong with not marrying and staying together. You just need to get a job sooner rather than later and keep assets separate. Similarly, there's nothing wrong with splitting if he isn't willing to marry. Of course, with kids in the mix then things do need to remain civil, but he duped you. It's his own fault.
If it was me in this situation, I'd find the deceit worse than the not marrying. If he'd been honest before kids at least you could have made a balanced decision. He purposely has strung you along to get what he wanted. At the best he's lazy, and at the worst a liar. Do these outweigh him as a partner and dad? Only you can decide.
Also, I haven't RTFT but regards surnames, what about a double barrel? If he doesn't want to marry but you have decided to stay together, it's the least he could do. However, part of me suspects his ego wouldn't like that very much...
It's your call. Take time to think about all scenarios and go with what is right for you in the long term.