"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.