OK so a few things here.
Your DH could apply for PR under Step Parents Parental Responsibility. My DH and I looked into this a fair few years back (I decided I really didn't want it in the end). This means that should it be granted then he would be financially and morally responsible for your children in addition to you and your ex H.
From a practical point of view - why does he need it? DR's and Dentists are quite happy to have consent given - infact my DS has never had my name and I have never been questioned. My DH has taken him to DR's appointments and never been questioned. In an emergency - he still wouldn't need it as emergency care would still be provided.
He is happy to have it now BUT if you split with him then he is financially still liable. Does he understand that you could still apply for maintenance payments from him as well as your ex? I know when we are in a relationship that we say we wouldn't do that but you could and there are no guarantees that you won't.
You comment on the courts maybe not liking the 2 against 1 but again, what if you split? Are you prepared that they could have a casting vote against you at every major decision? Are you prepared that you may only see your children 30% of the time? That could happen, your ex has contact and now your new ex wants contact, that means your 2 ex's could get more time combined between them than you - because with PR comes the legal right to apply for contact.
FWIW my DSS lives with us and if something happened to his dad, my guess is that he would still choose to live with me, I don't have PR (he does turn 18 later this year anyway). If that is his choice then I would of course still offer the same support as I do now, not because I have to but because I would want to.
I think you need to be really honest with yourself and understand exactly why you feel the PR is important?
The name is a very easy fix, change your DH's and LO to your other children's name. Easiest and simplest answer without any upset or conflict with anyone.
My DGS's both have our family name not their DF's, his mom changed his name to hers when he was 13 (bit messier than your situation) but he resents it and doesn't feel like he wanted the children to have that name as he doesn't really feel that it belongs to him but didn't feel that his dads belongs to him either - he plans on changing to our family name should they get married.