the 'ke' or 'ike' ending is a popular diminutive in many European countries, and I found
Evike, Hungarian pet name for
Eve or
Eva, in the database. I had a quick look but couldn't find an obvious 'ell' name for Ellike to be a nickname of, but BtN's Hungarian names list is by no means exhaustive. So I'd say it's probably a nickname for some Hungarian 'ell' name - possibly roughly equivalent to
Ellie in English.
:-)