Pronunciation is a matter of family tradition.
The way the old folks pronounced it is the correct pronunciation. As Hargreaves is an English name, one would expect to find clues as to its pronunciation in English usage. So both common pronunciations of Hargreaves are consistent with ordinary English usage. Most Hargreaves, or descendents of Hargreaves, can trace their roots to Lancashire or Yorkshire. It has been suggested that the Lancashire Hargreaves incline towards the 'e' pronunciation and those from Yorkshire incline towards the long 'a' pronunciation.