I currently have the "Supporter" badge due to donating a specific amount in the past. That said do I have it more than once that people misunderstand me for a Staff-member (Actual Spigot Support) due to the name of the label being "Support". My suggestion is to rename this, to prevent any future confusion and to distinguish donators from staff/actual support.
In the 6 and a half years I am a member here (I don't remember how long I have the badge), this only happened a couple of times, and it always was pretty hilarious. If somebody is incapable of contacting staff the proper way, the content of the inquiry would most likely suck anyways, so there is no real harm here.
I mean... people are dumb. Supporter doesn't mean "Support Team" nor "Helper" or some shit... I guess renaming it to donator would help in your case, but I'm sure this isn't frequent.