Frodo said "These are
High Elves! They spoke the name of
Elbereth!'" Was Frodo's assumption correct?
Yes
When
Tolkien wrote this statement, back in
Three Is Company, there was, as yet, no
"Sindarin" language, and the name
Elbereth became a Noldorin name [it had been an "Ilkorin" name, of
different meaning, when it referred to one of Dior's sons, for example].
So Frodo appears to be correctly identifying the Exiled
Noldor at this point, who are High Elves and used a Noldorin form.
After the history of the
languages was revised however, the name
Elbereth became Sindarin. JRRT did not alter Frodo's statement, but within this scenario it could be said that Frodo correctly pointed out that these
Elves were High Elves, who then make it clear to the reader that they are Exiled Noldor.
This seems possible 'cause
High Elves, while it often refers to the Noldor in a
Middle-earth context, appears to have another application, in which it is basically equivalent to the term
Eldar as defined in The Return of the King [the term is defined a bit differently in the constructed Silmarillion].
I note Hammond And Scull (
The Lord of the Rings Reader's Companion, chapter
Three Is Company):
"(Elsewhere Tolkien equates Eldar with the High Elves (see note for p. 43), . . ."
Christopher Tolkien (
Introduction to
Children of Húrin):
" . . . and they are called the Eldar, the Elves of the Great Journey, the High Elves: distinct from those who, refusing the summons, chose Middle-earth for their land and their destiny. They are the 'lesser Elves', called Avari, the Unwilling."
That's my interpretation of how to view Frodo's statement, anyway.
Unless I'm wrong!
Then never mind.