Question Author
I just can't go for HARE. Why would Hair be the most important thing on the head?
Whereas MANE sounding like most important thing (MAIN), at least addresses "the most important thing".
Importantly too - I found reference that MANE not only refers to animals necks, it can refer to an unruly mop of hair on humans too.
So thanks everyone but I must go with MANE (unless I hear anything with better explanation)