Don't be ashamed to call yourself a programmer. Alex Stepanov, who created hundreds of billions in value by creating the C++ stl calls himself a programmer.
I find that even saying "I'm a programmer" in social settings triggers my counterparty to frantically start scanning the room for anybody else to talk to.
In social situations when that comes up I usually say something like "I work for <employer>" and then immediately try to change the subject.
I got the exact opposite advice decades ago if you want to remain technical. If you start becoming the company expert on their business processes as a programmer, time to move to a new company.
That served me very well and I remained a programmer for my whole career.
I think this is very good advice for many programmers. I think a lot of programmers become stagnant in sone company because if the phenomena you describe.