There is a field for the creator, but not every common name has information stored in that field.
Just to be clear, the source is not the same as the creator. It’s similar to a new taxon – e.g. I could be the creator of a taxon, but the source of the taxon is POWO.
There is already a request to make it easier to include sources for common names, you can add to the discussion there. This request is independent of that one.