Antonius is correct - well done for leaving the H out! - and for David the easiest and most obvious solution is to add -us and get Davidus.
I'm not a catholic - not an anything, actually - so I'm not familiar with the Latin version of the Old Testament. My impression is that they tended to leave Hebrew names unchanged ... however, old baptismal etc registers would regularly use the Latin forms of all names, even Germanic ones like Edward, and achieve this with a well-placed -us. Or, for girls, a well-placed -a! neither of these endings would have been used when actually saying the name; little Davidus and his sister Philippa would have been David and Philip, believe it or not, but the formal version was used for official purposes (hatch, match, dispatch).