Starfleet / KDF should address you as your rank. For exmaple : "Vice Admiral, I have a new mission for you."
Your crew should always call you "Captain" since you're the Captain of the ship regardless of your official rank. (You're the acting Captain of the ship even though you're just a Lieutenant) For example : "Captain, we're being hailed by the Gorn commander."
Planetary Governments should also address you by rank only. For example : "Rear Admiral, I'm glad you're hear to help. We could use some Shield Generators."
You know, come to think of it, is that how it works already?
My biggest complaint about ranks is the whole Rear Admiral Upper Half, and Rear Admiral Lower Half nonsense. No one should ever refer to you as that. How about just "Rear Admiral" or even just "Admiral."