Changing name

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I’ve been divorced for 3 years and I’m still using my married name. Originally it was because of sharing my name with my children, now it’s that and a degree of lethargy and confusion. Children don’t have much contact with their dad (because he can’t be bothered) and have both said they’re happy for me to change my name back to my maiden name or to double barrel it. Dd is 18 so could change hers but says she likes her name and it’s her identity, fine. Ds at one point said he’d like to change his to be double barrelled. He’s 15 so I guess he’d need his dad’s permission , I don’t suppose he’d mind but he’s unlikely to put much effort into anything involved to give consent.
I feel like I need to make a definite decision as I don’t know who I am.
If I double barrel, do I need to do it by deed poll? What about the children if they want to change and what permission does dad need to give? Any thoughts on the pros and cons?

I’ve been thinking about this. I’m not yet divorced but I guess at some point I’ll go back to my maiden name. I don’t know whether the kids will want to double barrel - we’ve discussed it not in the context of divorce and they said no but maybe if I’m changing mine they might prefer to..

I think my ideal would be I use maiden name and double barrel the kids, but it depends on your feelings.. how do you feel your name makes up your identity? I think at 15 if dad won’t sign then just use it non officially and then change officially at 18. But I’m fairly sure it’s only a form to sign?

Thanks for your reply @IndraOnTheMountain I need to do more research and thinking!