"Heim" definatly means "Home" and comes from old scandinavian/german. e.g. Muspellheim (home of light and heat) and Niflheim (home of dark and cold)
If "Shy" is also supposed to come from something scandinavian/german I have no idea what it should be. It still could however. In todays english "Shy" generally means "timid" or "in lack off", but if shy holds this meaning in this case I am not sure of.
I wonder however if that "Shy" could be a prefix coming from the name shylock? In Shakespeare's play "The Merchant of Venice" the jewish merchant is named Shylock. But I do not know what his name means.
Else the name should mean something like: Timid home