I went to school with a ton of Adrianas. It wasn't as common a name as, say, Ashley or Brittany or Emily, but I lived in a district with a high Hispanic population so a lot of girls were named Adriana, Mayra, and Araceli (the most common Spanish names among them). None of the girls named Adriana had a nickname - they were all called Adriana, and it wasn't difficult to say all at once despite being 4 syllables. It's a good, strong name to have.
I can't really comment on the maternal vs paternal grandmother thing, though. Sorry.
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