How do we end up with three vowels at the end of Περικλέους? (Greek)

Question

According to Wiktionary, the genitive of Περικλῆς, or Περικλέης, is Περικλέους; and similarly, that of Σοφοκλῆς, or Σοφοκλέης, Σοφοκλέους.

Question: How do we end up with three vowels, εου, at the end of these genitives? (Or morae if we are going to say ου is a vowel.)

Background

The last vowel, I venture to guess, comes from -ος, the genitive singular suffix for third declension nouns. I know that it sometimes combines with a stem ending in a vowel and undergoes a change, as in γένους from γένεος.

But to have three vowels together, we would need a stem ending in two vowels or somehow get an extra vowel in there between stem and suffix.

According to Wiktionary, the etymology of Περικλῆς is:

περῐ- (peri-, “very”) +‎ κλέος (kléos, “fame”) +‎ -ής

Could it be that between εο (from κλέος) and η (from -ής), we somehow ended up with a stem ending in two vowels?

Relevant too seems the case of of Σωκράτης. Its stem is Σωκρατε(s) (according to Mastronarde's Introduction to Attic Greek). The (not necessarily etymological) operation that takes you from word to stem is: (1) remove -ης, yielding Σωκρατ, and (2) add ε(s), yielding Σωκρατε(s). The same operation on Περικλέης gives you Περικλεε! Or at least there is some sort consistency here.

I would note that the question above on the genitive recurs for the dative and the accusative as well, e.g. Περικλεῖ and Περικλέᾱ, where we get three morae at the end, if not vowels. Compare ἀσπίδι and ἀσπίδα; Σωκράτει (Σωκράτεϊ) and Σωκράτη (Σωκράτεα). (Note: I struck Περικλεῖ because it does not have three morae.)

Answer 1

These names are compounds of κλέος, earlier κλέϝος (klewos). This is a neuter s-stem, like γένος. So the gen. sing. is *klewesos > *kleweos, regularly contracted to κλέ(ϝ)ους (ε + ο > ου). (Αs it happens, κλέος is attested only in the nom./acc. sing. and plural, but the missing forms can be reconstructed on the basis of other words). The only irregularity is the nom. sing. in -ῆς, which appears to be borrowed from the masc. first-declension nouns, by analogy to the many masc. names of this type.