Where does “Досай” come from?

Досай (Kazakh) comes from Kazakh ай, from Proto-Turkic *āy — moon.

Ancestry of “Досай”, step by step

Досай traces back through two separate lines of ancestry.

via Kazakh ай

StepLanguageWordMeaning
1Kazakhайmoon; month
2Proto-Turkic*āymoon

via Kazakh Дос

StepLanguageWordMeaning
1KazakhДосfriend
2Classical Persianدوسْت—
Every word from Proto-Turkic *āy →Every word from Kazakh ай →