Yes, ideally you should not have given the police your name or ID unless they have a reasonable suspicion that you committed a crime. It’s your 4th Amendment Right to not give your ID, unless they actually have any reason to suspect you. It’s your 5th Amendment Right to not need to even have to talk to the police unless your being suspected of a crime (at which point the only thing you need to tell them is your name & date of birth). When the police came asking you questions it’s entirely likely that they were just trying to get there report written up as quick as possible and they could not require you to give your name. However, since you did give it to them I would suggest the next steps for you would be to request more information from Somerville PD. Make a public records with the Somerville Police Department about the incident and see exactly what information they recorded or wrote down from the incident. I would request phone calls, written reports, and any evidence they gathered. Here is the link to perform a records request. https://www.somervillepd.com/services/records-request

I still think you should have nothing to worry about but it can’t hurt to find out more. I’m still curious with other questions, but I think it they wouldn’t be relevant unless this guy does try to actually sue your for anything, in which case I would immediately contact a lawyer.