Even beyond names, I haven't come across much of true abbreviations. Sure enough, in a religious context in Sanskrit, one comes across interpretations based on the constituent phonemes (or sometimes even less: the holy particle Om has been construed as a + u + M instead of what it possibly originally was: an old particle representing assent), but the contituents are then themselves glossed rather than treated as initial phonemes of glosses, though again there may be some ambiguity sometimes. Loss or retention of affixes and reduplication of initial segment in morphological constructions I am treating as a different phenomenon.
How old is the Hebrew use of true (as opposed to reinterpreted) abbreviations in any context? (i.e. what is the oldest, possibly religious text, which uses it). Is the particle ja or ya that stands for God in many hebrew names (e.g. in Abijah) a regular root used in its grammatically proper morphology, or is the beginning of a tend towards circumlocution through abbreviation?
An abbreviative system of course makes the rebus principle, and hence alphabetic writing, easier to discover; but Hebrew, at least in the form we know it, may be too late for that explanation to work.