a lot of people here have the wrong impression that I am still allowing myself to be abused and that I am still drawn to him
I do not think this, but I do think some of your posts lean towards the dangerous assumption that you can engage with him according to normal human decency/morals and logic. This is TOTALLY understandable - it's so much of a given/something we take for granted to such a degree that you probably don't even think about doing it - it's just normal. I never ever thought about it before I learnt how abusers tend to operate.
If he was a reasonable person, then it would be a totally reasonable thing to ask him to sign off on a name change and/or even parental responsibility (though, in English law this is not actually a thing) given that he's expressed that he finds the children difficult to cope with and doesn't enjoy being a father.
It would also be totally reasonable to say yes wouldn't it be nice for the children to have the opportunity to have a relationship with their father, it seems a shame to cut that off without finding out if it's even a possibility.
The problem is that he is not a reasonable person. He is an abuser. And no, I am not saying abusers are 100% terrible people. I understand that extremely well. I have loved an abuser too, and there are abusers in my family who I have complicated feelings about. It's honestly not that I think they are terrible or deserve to be written off - it's just that you have to be incredibly careful when dealing with any kind of request or power dynamic with them. You cannot assume that they will operate in a fair or reasonable way. It is ALWAYS about what's in it for them and they see EVERYTHING through a lens of winning and losing. Most people have empathy and a sense of fairness, a sense of perspective, can let things go, and would at least try to see a little of the other person's side even though most people are of course biased towards themselves. Abusers are not like that - they are incredibly sensitive to what they perceive as a loss of power and will latch onto it. It's probably some kind of trauma response. I don't think it's conscious at all, it's something deeply embedded in the way they see the world. They tend to assume that everyone else thinks about things the same way - they are often paranoid and suspicious or tie things up in knots unnecessarily, out of a fear someone else might screw them over when most people have no such intention.
men can only worm their way back in when the woman needs or wants them in some sort of capacity
You have convinced yourself you are immune to him, and I completely believe that you're immune to him ever tempting you back into a relationship - but I think you might want to think about whether there ARE things that you still want from him - you mentioned wanting some possessions, which might be worth trying to get, but be careful - you want his permission to change the children's names, you may at some point need his cooperation/agreement for accessing e.g. an emergency passport, or if you ever decided to move abroad (unlikely though that may seem right now). So my main thing would just be to say be bloody careful and be aware he's highly unlikely to play by the same rules as anyone else would. You can't beat him at his own game, but you do concede something to him by making him aware that you want something he has the power to refuse. So think about whether what you want is worth the risk of that and whatever he twists it into.
Sentimental possessions - it probably is worth asking for these, IMO, especially since he likely already knows you will want them, and most likely has no use for them and/or giving them back will make him look gracious to outsiders, so has a benefit for him unless he thinks that he can use them as leverage against you.
Children's names is much less clear cut - this doesn't really carry any benefits for him, if he voluntarily signs things like this over, then he can no longer be the "sad, ostracised dad whose crazy ex won't let me..." - he's the guy who voluntarily abandoned his kids, which is a much less favourable impression of him. You can ask, but I would be cautious about doing so.
Some part of you also sounds like you're wanting contact between him and the children if it would be possible from his end. My assumption is that this is based on either a general belief that it is better for children to have contact with their father than not, or that they may be harmed by his absence. Or, possibly, (maybe and?) it's rooted in a niggling feeling that you ought to do as much as you possibly can to facilitate this before drawing a line under this, that it's partially your responsibility as a mother to enable and encourage a positive relationship with their father, possibly some guilt over having "chosen" a father who turned out to be abusive and later absent.
My advice in general to this would be just to 100% drop it as a responsibility of yours. Your responsibility to your children, IMHO, is YOUR relationship with them. His relationship with the children is 100% his responsibility. Your only responsibility in relation to him is not to be negative about him towards/around the children, and of course, to extricate yourself from his abuse as you have done brilliantly. If he does not want to arrange contact, then you should not look into arranging it for him. If he does not know how to arrange contact, don't worry about it. It's on him to take the initiative to find out. If he has got himself blocked due to his own harrassing behaviour, again, that is his own problem. It is likely not impossible for him to get a message to you somehow if it turns out that he does have a burning desire to see them, and of course he could always apply for contact through the family courts. In the meantime, I think your assumption (that he can't be bothered) is highly likely to be correct. It's sad, and yes it might harm them emotionally. But you cannot control his decisions and his behaviour, and ultimately, any harm they experience from his absence is likely to be much less than any harm they would experience from witnessing or experiencing parental abuse.
It is not your fault that he is a poor father. You haven't done anything wrong, and there is nothing to put right.