Thank you for this question, it actually led me to double check my answer and I see that things have changed.
Previously, the answer was simply, no. An account was tied to the name it was set up with.
Now I see there is an option under the business settings to transfer ownership of the account.
I assume this is typically meant for when someone sells a business and they want to transfer the square account with it.
However, I see no reason why you couldn't use this to change the name on the account as well.
Although, there may be some trouble with using the same SSN. Worth a shot to try it.
Here's the help article about this:
https://squareup.com/help/us/en/article/7675-transfer-ownership-of-your-square-account
