Cant you just check those locations off as Private. https://docs.storelocatorplus.com/blog/q-how-can-i-mark-a-location-so-it-does-not-show-up-in-the-results/
You can add another location with the same exact name. Just add it the way you would add any location to your user interface. The geocode will be contingent on the address not the name.
Please follow the Posting guidelines and reiterated here. provide us with a screenshot of the plugin environmnet under the INFO tab of the SLP plugin. We do not know what versions, add-ons etc that you have active.