One thing we know for sure, is that the Old Ones used a definite lettering system with a fixed transliteration scheme into the latin Alphabet.

Lovecraft said Cthulhu was pronounced "k-tuee-tuee". When asked why he spelled it that way, he said he had no control over how cultists spell their gods' names.

It's probably safer to misspell it. I imagine it was intentional to avoid unexpected consequences.

Betelgeuse! Betelgeuse! Betelgeuse!

Cthulhu's illiterate for all we know.