There were four "famous" Korinnas in the Greek antiquity:
the famous doric poet from Tanagra,
the lyric poet from Thespis and
from Thebes, another lyric poet.
I think LGPN covers names of everyday people and not of known people which are easy to find in other sources (such as names of people in mythology, heroes, etc.) so thats possibly why there is only one Korinna
According to the book "The Logos within the word" (ISBN 960-316-347-3), the ending "-inna" derives from the word "innos" ("incomplete").
As far as I know, the name KORINNA
is rare in modern Greece, I personally know only two. I really doubt the name KORE
is in use at all (or if it is it must be extremely rare).