For starters, Jesus was not a Christian (he even departed from normative Judaism of his time in a massive way). Why is then necessary to call yourself as such? In fact, all labels you call yourself, including your very legal name, were attached to you by those who came before you, that is, already labeled and indoctrinated people.
As for reincarnation, the way it is popularly believed in in (predominantly) Asia is the equivalent of misinterpretations you have found in Christianity. The actual personal reincarnation does not take place. Who reincarnates is "I". Every living thing has the same identical first person perspective. And I guess you are familiar with Ex. 3:14 and the way God addresses himself. Now, connect the dots.
There is a lot to be said about this, so I just leave here some links to what I've already said (read "wrote") on this topic ;)
https://medium.com/@senderspike/no-one-here-gets-out-alive-f7a2a1db75
https://senderspike.medium.com/mystical-union-f8bec38f7d53
https://senderspike.medium.com/the-way-of-torah-1fc65d8a36c9