If you want your resurrected self to be "you," then it's up to you to decide if your values are satisfied. A soul is something you made up. You are not barely aware of something simple and fundamental. The heuristic you use is not an approximation for something nicer. It's just what it is. If you value having simple and elegant values, there's not much you can do besides abandoning that one altogether.

If you just want to know what you would consider your resurrected self, because you have never been in that situation so you're not sure what you'd think, I'd say most of it is about memory. If someone with a completely different personality inherits your memory, I think they'd probably think of themselves as "you". Similarly, if your memory was replaced with someone else's, you'd start thinking of yourself as them. You would have a different personality, but you'd likely think of it as having changed, not being someone else altogether. That's just my guess, though.

If you want to resurrect a loved one, you should probably restrict them to also having a similar personality.