Johns Hamilton Gray

John Hamilton Grays sounds more correct. The three parts of the name act together as a single subject, so it makes more sense to put the s at the end of the noun rather than somewhere in the middle… Grammer has never been my strong suit though.

It’s definitely “John Hamilton Grays”, which you could shorten to “We had the Grays over for supper last night” (“We had the Johns over” just doesn’t sound right!) as opposed to “Governors General”, which would contract to “We had the Governors over last night”.
My simplified rule is that you pluralize the part that can stand alone.
The official rule (http://en.wikipedia.org/wiki/English_plural#Plurals_of_compound_nouns) is:
The majority of English compound nouns have one basic term, or head, with which they end, and are pluralized in typical fashion e.g. “able seaman” = “able seamen”
A compound that has one head, with which it begins, usually pluralizes its head e.g. “son-in-law” = “sons-in-law” and “attorney general” = “attorneys general”
There are also some with two heads, where can pluralize both, such as “sons of bitches” and “heads of states”, or you can leave the second head singular.
Of course, as time passes, everything will eventually standardize to the “regular” form with the “S” at the end, leaving us with “governor generals” and “son in laws”. Pity.

Depends whether dinner was at a brothel.

Perhaps (only in this instance) you should consider using the phrase, ” John Hamilton (Shades of) Gray” or maybe “Shades of John Hamilton Gray” This is important because there may be more than two. Nuance is everything!