Plymouth and Rhode Island merge?

I'm not necessarily familiar with the situation OTL as to why Plymouth merged with the Massachusetts Bay Colony, though if I remember correctly I think Rhode Island was supposedly more liberal than the puritans in Massachussetts and Plymouth.

Regardless, what would the effects/consequences be if Plymouth and RI combined rather than Plymouth and MA bay? I would imagine, presupposing butterflies are not too intense, this state would probably be somewhere between CT and MA in population today, but what would some other effects be? What would this colony/province/state be called?
 
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