Not a traditional zombie
There are many ways to label this kind of creatures. Zombie doesn't quite fit, as they normally only regenerate once in the sense that they are coming back to life. But their bodies are still the way they were when they died and they normally can't regain lost limbs. Zombies tend to be quite dumb, too.
Many opportunities depending on the style
Depending on the style of the regeneration you could draw inspiration from different existing works of fiction. The names however should be used carefully. You want to show some measure of originality to make them your own.
Frankenstein for example created a monster from different body parts. If your character can simply take limbs he finds lying around and sew them to his body this might be an ideal source of inspiration.
Doctor Who can regenerate completely, too. Each time in a completely different body, though and as far as I remember there was a limit for how often timelords can normally regenerate.
Markus Heitz used the term "Soul Wanderer" in his book "Exkarnation - Krieg der alten Seelen" (as far as I know there is no english translation of this german book - it basically means "excarnation - war of the ancient souls") for a concept where souls come from one source and normally return there - but there are a few who can inhabit a different body once their old one dies and thereby "escape" the normal cycle of rebirth.
Vampires can also regenerate as long as there is no sunshine and there was no silver or holy symbol involved. The same applies to werewolves and other werecreatures.
Often Fey, Elves and other magical creatures like dragons, anthropomorphic unicorns (Elder Races Series) are described as having heightened regenerative abilities - what looks to normal characters like a sure death may feel like an inconvenience to magical creatures of any kind.
Necromancers are often playing with the dead. Ensuring yourself won't become one of them is just a necessary and obvious step. Often this can result in a lich, who may never die as long as you don't destroy his phylactery.
The anime Ajin has a complete recovery, no matter how you kill such an Ajin. Except for one thing: they have a shadowy impersonation of their emotions that helps them regenerate and can only be seen by other Ajin. If one Ajin destroys the "head" of another Ajin it is killed and the person is really dead.
You could simply go with "immortal soul", "devil", "demon" or any other such, often evil, creature and just say that your version works the way it does in your world.
Conclusion - do what you feel is right
Choose a name and be consistent. Or don't choose a name.
Who says that the character has to know what he is?