My brother in Jesus Christ paperwork, even now there are already 236 active and formally-registered trademarks which have been granted involving "Jesus Christ", 18 if you limit it to "wordmarks." [0]
Also, as per the concurrent(?) edited-in last paragraph, the basic idea remains even if the scope is, er, less-grandiose.
There are a number of longer phrases which include the phrase "Jesus Christ" that are trademarked (either as logos or as phrases), but that is a very different thing.
So, you could start a new church and trademark "Terr's Church of Jesus Christ", as the trademark covers the organization, but you cannot trademark the name "Jesus Christ" itself.
IANAL but I don't think it'd be blocked for that reason: "Right of publicity" is a per-state affair, where it exists it may not be posthumous, where it is posthumous it may not include historical figures, and even if it could apply, there's there's no credible estate/heir of Jesus Christ with standing.
... But I gotta admit it would be amusing to watch someone try to fill that role.
As an example, see Pirone v. MacMillan [0], where there was no posthumous "right of publicity" for Babe Ruth's daughter to draw upon. (At least, not back then.)
[0] https://law.justia.com/cases/federal/appellate-courts/F2/894...
