I would offer Hristondilmë in Quenya, which translates to servant of Christ or devoted to Christ. Tolkien was actually a devout Christian and translated several prayers into his own languages, so we do have a word for Christ!
Name construction is Hrísto (Christ) + (-(n)dil) (suffix meaning lover of or devoted to) + më (a feminine suffix).
Do note, though, that the validity of -ndilmë as a suffix has only been attested once and in a contracted form, so it may not be completely accurate.
And, as always, I recommend a second opinion!