"Ive never been fully aware of his financial situation" you're about to have a child together! You SHOULD know exactly what his financial situation is! He's irresponsible and secretive - why?
I would not be at all surprised if when learning of the full facts of his finances (which you ABSOLUTELY should BEFOREHAND you make such a huge financial commitment with him as buying a house - to be honest you SHOULD have known this as soon as you moved in together, certainly before conceiving - assuming that was planned?) you were to discover:
1 he has a higher income than you thought - him SAYING he "can't" contribute more doesn't necessarily make it true
2 he has more debt than you thought
Crazy to do anything without getting the FULL information first.
"I know how much is his salary" from what he's told you or have you actually seen payslips - more than a couple?
You do understand you don't HAVE to buy a home? Yes renting is more expensive monthly but there are also costs and cons to being an owner too, maintenance and repair costs are solely yours to bear, doesn't sound like you can afford to do that - certainly you can't rely on him to cover such things!
We have an odd attitude to renting in this country, there are pros and cons to both renting/buying.
"What's the worse case scenario though? If he fails to pay, I pay it and end it." Actually worst case scenario is you bankroll him throughout your relationship, eventually split due to resenting this and he has at least half claim on a house you've mostly paid for AND are responsible for debts he's accrued!
"If no credit cards are involved, how can he acquire debt in my name?" Frighteningly easily actually. Not saying he is but I have certain relatives who are gamblers/con artists/fraudsters and it's CRAZY easy to get credit cards and other debt in the name of the person you're cohabiting with (even in the name of complete strangers to be honest). Happens all the time!
"The joint account would only be for his salary and the mortgage/bills." Do you understand that having a joint account with him legally binds you to him financially?
"We've been together for two years, dated for a year and moved in after that." It genuinely stuns me how quickly people move in together on here!! ONE YEAR is no time at all, especially given he has a child in the mix!
The first year-18 months of a relationship there's a combination of biochemical/psychological reasons why the rose tinted glasses are on, plus people are on their best behaviour in this period.
Quite honestly anyone moving in with a romantic partner earlier than 2 years into relationship ESPECIALLY with children in the mix is nuts!
But you are where you are AND pregnant too - again people seem to rush into this on mn, though when challenged there seems a higher than usual incidence of "accidental" pregnancies 🤔 which as someone who's had ONE themselves I do understand CAN happen, but not at the rate that's claimed on here!
Seriously - DON'T marry him, don't give baby his name, don't get joint finances with him, don't buy a house with him unless and until FOR A SIGNIFICANT PERIOD OF TIME he's SHOWN a major change in attitude and actions to you and how he handles money.
Quite honestly, if he apparently can BARELY afford his current responsibilities it's somewhat irresponsible to be having another child anyway!