There are many interesting zeta functions, and the Riemann zeta function is the most notable of them. It is natural to expect that people who ask questions about other zeta functions would want a separate tag, and indeed, only a very small proportion of the questions tagged zeta-functions are about the Riemann zeta function. I think it would be better to leave the tags separate and change the tag description for zeta-functions.
Update: I have changed the tag descriptionchanged the tag description.