***Corrected Post*** (sorry for the multiple updates Maggie)
British America was formally used to refer to the Colonies on the North American Mainland from 1607-1783. "British North America" was subsequently used informally for the British holdings (now mostly Canada) from the treaty of Paris in 1783 becoming more formally used with the publishing of Durham Report in 1839. BNA effectively ceased to exist when Newfoundland became a Dominion in 1907. With that said....
I think simply "Massachusetts", or "Massachusetts Bay" is appropriate for dates prior to 1776. I would similarly not be inclined to append British Empire after 'India' or "Australia", and in modern terms "Montserrat" would be preferrable to "Montserrat, British Overseas Territories". Do we use just "puerto Rico" or "Puerto Rico, USA" ?
I believe the correct formal names for Massachusetts prior to 1776 would arguably be:
1628-1686 and 1689-1691 Massachusetts Bay Colony *technically I believe it could be applied starting in 1624 with the failed Cape Ann settlement
1686-1689 Dominion of New England in America *This name was not widely recognized by the residents and lead to a number of revolts resulting in the reversion to Massachusetts Bay Colony- For simplicity I would suggest the use of Massachusetts Bay Colony be used during this short period as it is likely what the inhabitants continued to use.
1692-1776 Province of Massachusetts Bay
This of course does not settle issues of where the boundaries laid at any specific time as there were innumerable changes and disputed areas throughout history.
