For anyone else curious about the legal name change process in the US, this varies depending on state.
I legally changed my name doing it the court process way. My state didn't require the newspaper thing. Was just $83 to file and show up at the hearing, and it was done.
Where it gets really fun is I have an apostraphe in my last name, and in 2025 we still can't make web forms that handle it. Some allow it, some don't, and it causes mismatch issues all of the time.