"Varda" and "Vardo" refer to the same person: the Vala1 Varda.
The difference between the two words is a grammatical rule; it's essentially the difference between "Varda" and "Varda's" (as in "belonging to Varda").
I can't find a reference from Tolkien himself at the moment (someone who has History of Middle-earth V may be able to provide a quote from the discussion of Quenya phonology in that volume), but this translation by Ardalambion2 translates the line (emphasis theirs):
Vardo tellumar nu luini yassen tintilar i eleni ómaryo airetári-lírinen
"under Varda's blue vaults wherein the stars tremble in the voice of her song, holy and queenly": Vardo is the genitive of Varda
In comments, Sean Duggan points me to a Wikibook on Neo-Quenyan morphology which describes the genitive rules for different suffixes. The relevant rule is (emphasis theirs):
In words on -a this final letter is replaced by -o:
máma "sheep" → mámo
Genitive case, if you're not a grammar nerd, is the possessive form of a noun.
Varda and Elbereth are both names for one of the Queens of the Valar, though Varda is her "proper" name and Elbereth is more of an epithet, identified in The Silmarillion:
With Manwë dwells Varda, Lady of the Stars, who knows all the regions of Eä. Too great is her beauty to be declared in the words of Men or of Elves; for the light of Ilúvatar lives still in her face. In light is her power and her joy. [...] Of all the Great Ones who dwell in this world the Elves hold Varda most in reverence and love. Elbereth they name her, and they call upon her name out of the shadows of Middle-earth, and uplift it in song at the rising of the stars.
The Silmarillion, Valaquenta, "Of the Valar"
1 Singular form of "Valar." At this point you may be thinking to yourself "that seems awfully grammatically pedantic." Yeah, it's going to be that kind of answer
2 Ardalambion is a fansite maintained by Helge Kåre Fauskanger, a Norwegian philologist3 and Tolkien enthusiast. His project is one of the most comprehensive sources on Tolkien's constructed languages
3 Person who studies the historical development of languages. Tolkien was also one, you won't be surprised to learn