What is the translation for the girls name "Altynai", I believe it is
Russian or Kazakhstani - what does it mean?

The name Altynai means "golden moon" in the Kazakh language.

Here is a citation from a page describing travels in Kazakhstan:

"Aygul sang a love song called 'Altynai'. This song is addressed to a
girl whose name means golden moon."

BBC
http://www.bbc.co.uk/nomad/Pages/day37.htm

Variations on this name include Altinai, Altuin, and Altynay:

"Altinai, Altuin - golden moon 
 Altynay - dear, precious, golden; Altinay: golden moon; Altyn: gold"

Kazakhstan and Adoption
http://www.geocities.com/kazakhstan_adopt/names.html

"The range of personal names Kazakh people have is very wide but is
not limited by national or racial prejudices. The process of
engendering new unique names is observed within centuries. Kazakh
people do not have specially devised names. All names come from their
life and events that accompany it. Sometimes names were given in
accordance with the circumstances in which the child was born: during
the roaming from place to place or in accordance with some other
events...

Female names are connected with beauty, subtlety, grace:

Aisulu - lunar beauty
Altinai - the golden moon
Meruert - pearl
Asembala - wonderful child."

Personal Pages of Alexander V. Mogilev 
http://www.vspu.ac.ru/~mog/interex/Kazakh/AMAIMENA.HTM

Search terms used:

"altynai" + "meaning"
"altynai" + "means"
"altynai" + "the name"
"names" + "kazakstan"
"names" + "kazakhstan"
"kazak" + "golden moon"
"kazakh" + "golden moon"

I hope this information is useful. If anything is unclear, or if a
link does not function, please request clarification; I'll be glad to
offer further assistance before you rate my answer.

Best wishes,
pinkfreud

Very quick answer - thank you.