"
Li am" does mean "I have a people" in Hebrew, but I have never heard of it as a given name (ask
Noa if he has, as he lives in
Israel). It does not seem to fit into one of the ordinary name giving schemes, but nor does ELIAM, which I haven't heard of either. The
LI part can hardly be be a short form of
ELI (my God) the two only have the I in common, which is a 1st person singular possessive suffix (my). I'm afraid some else has to help here. Sorry.