I’ve done a bit of digging and feel confident saying that Adian is not a Russian name.
Russian figure skater Adian Pitkeev is of Kalmyk descent.
https://en.wikipedia.org/wiki/Kalmyk_peoplehttps://en.wikipedia.org/wiki/Oirats
I found this interview with him and among others things he mentions that:
‘’ - Who named you Adian? Do you know what this name means?
- It was a friend of my grandpa's family with my grandma, Dyugev Adian Nimeevich, a famous doctor in Moscow, a doctor of medical sciences. Therefore my father decided to call me Adian, so that I, as he says, would not forget about my Kalmyk roots. And my mother also liked this name. And it translated from Sanskrit as "sun".’’
http://www.goldenskate.com/forum/showthread.php?55608-Interview-and-Translation-Adian-Pitkeev I don’t know enough about Sanskrit to confirm or refute this claim.
The mathematician’s surname could be transliterated as Adian or Adyan and is apparently of Armenian descent.
https://en.wikipedia.org/wiki/Sergei_Adian
I have found Adyan in these articles about Kalmyk names
https://en.wikipedia.org/wiki/Kalmyk_names and
https://en.wikipedia.org/wiki/Akora_Khattak#Akhund_Adyan_Baba_Seljoki
As a Bosnian name it is used by Bosnian Muslims and probably has an Arabic or Turkish root.
http://www.knjigaimena.com/?znacenje-imena-Adian - this Bosnian name website claims it is of Arabic descent, meaning ‘religious, devout’. Again I don’t know enough Arabic to confirm or dispute this.
I found this Iranian film director whose surname is As’adian -
https://fr.wikipedia.org/wiki/Homayoun_As%E2%80%99adian.
Hope this was at least somewhat helpful to you. Maybe someone more knowledgeable in these languages can help.