Don’t assume that his surname was Robinson when he emigrated to the America’s.
There are a myriad of reasons why the original surname may have been changed, from literacy to hand writing to accent.

I had the same problem with my family surname. It’s been spelled one way in Australia since c1860. On shipping records it’s spelt another way ( the sticking point) back on the IOM it was spelt another way. (Yet that has also changed to the current spelling)
As the ship was English we assume the accent of the Manx family sounded different to the English person taking names and it was misspelled.
Once arriving in Australia the shipping officials would have been from another part of England and again not understood the accent.

If you have a local family history society go and visit them with the information and documents you have.
They are wonderfully helpful and have all sorts of sneaky ways to find information and the experience to reinterpret spelling and handwriting.

For example: my ex hubby and children have a simple surname we assumed was English, research was easy and discovered they were of Scottish decent. Met a neighbour in the bush with the same surname.... assumed that they may be related as their son looked like our son. (And the son could be mistaken for my child and has been, that’s how similar the features were)
Spoke to the father... family are of Danish decent. Danish surname changed by officials of English birth at the docks in NSW.
None of it is on purpose it’s just the different accents and education levels that were around in those days.