Renaming Hue groups won't update the Hubitat name--that's set when the integration app creates the device and won't change unless you do so manually. I'm not sure how Hue groups with only plugs or a mix of bulbs and plugs show up or if Hubitat's integration looks for lights and then shows only those groups.
I don't want to plug my own app here, but I recently released an open-source Hue Bridge integration [RELEASE] CoCoHue: Hue Bridge Integration (including scenes!), and I know it doesn't don't do anything special to filter out plugs if it just gets presented by the API as a regular device ("light") or group. Hubitat has barely updated their integration since it was released, and while they may decide to add in this feature if theirs needs to explicitly whitelist certain categories of devices, I can say that I'd be willing to work with you if mine doesn't work, but I assume it already should. 
