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nitpicker – “These are not exceptions at all.
these names are compounds with more than one part. not two names.”
The Noda B’yehuda provides these examples, look it up.
“
very interesting. in fact amazing.
the mahrshal (as i think I remember quoted by rav yissachar frand)
said there were none. so he didn’t see it same as as the noda b’yehuda.
to haleivy.
I am not sure why you addressed your comment to me, but I agree completely. My own second name is another example and I am sure it also was just a nickname, never used formally, in previous generations. As you say, these names eventually became actual
names used to call up or in shtaros. Still later they became stand-alone names in their own right, without the name they used to accompany.