The two words are unrelated to each other and are pronounced pretty differently in Greek. Cleopatra's name is not written as you think it is, the name is Κλεοπάτρα (Κλεοπάτρη), from κλέος, "glory." Clio, on the other hand, is written Κλειώ, is unrelated to κλέος, and is pronounced differently. Generally in Latin the ει diphthong was transliterated ī with a long vowel to match the diphthong, whence the spelling came to English and most other European languages. Thus Clio for Κλειώ, Clitus for Κλεῖτος, and Darius (the stress goes on the penult) for Δαρεῖος