The first and probably the most important point is that the "plantations" in Providence Plantations has nothing to do with slavery. That's a meaning of the word that only became current maybe a century or more after Roger Williams named his little colony in the early-mid 17th century. In the 17th century a 'plantation' was what we'd now call a 'colony' or a 'settlement'. The 'plant' in plantation wasn't (or at least wasn't primarily) a cash crop you were growing but the people you were inserting onto the landscape.
Yet that isn't the end of the story. Not by a long shot. Because Rhode Island is probably the most important slave state outside of the Old South, not only because it had a reasonably large slave population for New England but because of the pivotal role its merchant community played in sustaining the slave trade.
There's still a decent amount of controversy among historians about why slavery developed in the American South but not the North. Clearly, climate and the cash crops the climate made possible played a very big role. But there's still a good bit of contention about what role the different settler societies played in the process -- different religious professions, different modes of family transplantation, different attitudes toward work and so forth. My take was always very much on the side of believing that the New Englanders didn't get into slavery mainly because they weren't able to.
There's actually a letter from the 1630s I found in the course of my dissertation research in which an ancestor of the Saltonstall family proposed starting a war with the Narragansett Indians in which the English would enslave the Narragansetts en masse and swap them for African slaves from the Caribbean. It was a crazy enough idea at the time -- though something like this would happen in the late 1670s -- that there wasn't any discussion of how this would be organized financially. But the gist was that the Narragansetts would be shipped off to the Islands and replaced with African slaves.
In any case, for a host of reasons, by the 18th century there was significant plantation slavery (in the more familiar, modern meaning of the term) in Southern Rhode Island and the Rhode Island transatlantic merchant were the dominant players in the North American slave trade.
But here's the catch. Catch or irony, take your pick. Rhode Island started as two colonies. One was Providence Plantations, the settlement Roger Williams established in modern Providence along with a couple other small towns in what is now Northern Rhode Island. (If you have nothing better to do with your time you can read a journal article I published back in 1995 about one of these towns -- Warwick -- and the relations between settlers and Indians in the middle of the 17th century. Read the full version here in this anthology.) The other was Rhode Island, the folks living on Aquidneck Island, the main Island in Narragansett Bay.
The folks in 'Providence Plantations' were among the first principled opponents of slavery anywhere in the Americas, certainly in New England and by most measures everywhere in North America. Folks like Roger Williams, Samuel Gorton and a bunch of other guys who died more than three centuries ago whose letters and records I spent way too much time reading in my 20s. It's a fascinating legacy. The roots of slavery in Rhode Island, both as an internal institution and as a key force in the slave trade, came from the other original colony, Rhode Island and settlements in southern Rhode Island that were tied to it.
Because of my own background, I have a certain antiquarian interest in this old name. But it seems unambiguously true to me that purging "Providence Plantations" from the state's name, in addition to being a strike against the state's history, would have the perverse effect of silencing the legacy of the people who were anti-slavery long, long before many people in the Western World even recognized it as a moral question.
I get the reasons for trying to change the name. In modern English, 'plantation' means a southern estate with black slaves picking cotton. And the state is for the its living residents and citizens, not what someone who's got some relatively obscure historical knowledge about what these ancient names mean. Still, for all the reasons I've stated, if they trim the state's name down to just "Rhode Island" I think it will be a big mistake.