I dunno, I have heard the CG hail "breaking wind", "blue-bayou" and a dozen other stupid boat names. I disagree that they call "vessel hailing the CG" simply because they believe a name is "silly". I am almost certain that there is a protocol that dictates the usage of vessel name versus the generic response. I think the DSC / MMSI equipped radios will begin to address some of your concerns. In the meantime, I imagine there are opportunities to address rule-making authorities about the way the CG utilizes, and the FCC proscribes utilization of VHF frequencies. I don't know that anyone on SN really can make a difference (kind of reminds me of the Evans / AIS fiasco currently ongoing at CF)
Oh believe me, if I thought I could change anything regarding the CG, the effort wouldn't be wasted on this issue. I'd have much bigger fish to fry. Just a discussion.
However, hence forth, I deem the name of my vessel to be: Charlie Foxtrot 1386 Sierra Zulu. That will guarantee they address me as: "Vessel hailing Coast Guard".