What does Esmeray mean?
From Turkish 'esmer' meaning 'dark, brunette' and 'ay' meaning 'moon', giving 'dark moon'. (A 'sunbeam/beloved' reading circulates but does not fit the Turkish elements and appears to be a folk reinterpretation.)
What does Aydan mean?
Aydan is a Turkish/Azerbaijani name from 'ay' ('moon') plus the suffix -dan ('from'), i.e. 'from the moon.' Some sources list unrelated secondary meanings ('tall palm tree'), but the moon reading is primary.