Andy never called her a Cuckoo, One of the Three in One, or even just a Frost Sister. He figured out the subtle differences between Esme and her sisters. He did all of this because he knew what it was like to be overlooked because of a sibling.  So he wouldn't just assume Esme and her sisters were exactly the same. He called all of them by their names and never mixed them up.

Esme used to call him Andrew or Von Strucker until they become very close. Then it was always Andy.  She didn't make up some sort of nickname to antagonize him just his actual name.  In private she used to call him a asset or a associate but now he was always called a trusted friend.

Andy called her his best friend and she was one of the only people she trusted as much as she trusted her own sisters. They called each other trusted allies but they knew it was much more than that.

Sentinel Services and the other groups called them accomplices and tried to gather as much information as possible.  During the aftermath of a Hellfire Club assignment someone spread around a photo of them embracing amd enjoying a moment.  They became infamous ans labeled as love struck mutant terrorists with their own separate sets of personal problems. 

Which was actually pretty close to the truth. As time passed and their relationship progressed and matured what they called each other changed.  They changed along with the titles or names people placed on them including themselves.