This is an interesting mystery. I do not see variations of the name on a ship list and the earliest I see is in Pennsylvania from the 1700s. I think the name changed after the family arrived in Pennsylvania. Church records and ship lists often give useful information when they can be found and most Church records in the UK go back to the early to mid 1600s yet none pulled up on my search.

I do not know if you have seen this post or not but it might be of interest: http://mccumseyfamilyfootprints.blogspot.com

A good source to search multiple ship lists:
https://www.packrat-pro.com/ships/shipnamesMa.htm