I have done a fair amount of research and have found nothing specific about the origins of the name Azor Ahai.
Let's talk names
In general though, George R. R. Martin tends to create his names based on what he wants them to sound like. As per the below youtube video:
His main points within that interview are:
- He dislikes most Fantasy names (e.g. Riznakh)
- He has tried many methods of name creation
- Including those funny online name generators
- Baby name books
- He wants his names to be meaningful
- He wants his names to "fit" and "sound right"
- This can be based on whether the person is "important" or not, ethnicity / exoticness within the story, etc
- He bases his names on existing or historical figures, but usually gives them a slight twist so as to sound realistic and relatable
- John becomes Jon, Edward becomes Eddard, etc.
It's important to point out though that The George takes a lot of care in choosing his names, pretty much all of them are chosen with purpose and a huge deal of thought. It wouldn't be surprising if some of them had deeper philosophical or religious import to them.
See also: How did George R. R. Martin come up with the names of his characters? where @SystemDown points out about GRRM's name choices:
Coming up with the names for the characters is very tough. They can't be too weird (with like apostrophies and stuff) and they can't be too "real", like Francois or Patrick or any kind of a name that is tied to a place (Sandor being a Hungarian name was unintentional)
There is also an excellent break-down of GRRM's (possible) name choices and meanings in this article, published by Jamie Adair, in History of Game of Thrones, July 7th 2014, in which Jamie points out that some of GRRM's names are used in honour or as a reference to real-life people. But again, unfortunately, nothing specific about Azor Ahai
Come on, be specific
The closest break-down we have on the name Azor Ahai is from this thread on Westeros.org, where user "King of Winters" points out that
I always thought Azor Ahai meant "A Helper", Azor, "Favoured By God", Ahai.
I think they're from the Jewish language
As well as our own user Eran Medan pointing out in the comments that:
Yes, at least can confirm that as a Hebrew speaker, it roughly means "help my brothers" azor is עזור and ahai looks like achai/akhai אחיי, or a bit less similarly "the living" e.g. החיי but I have no clue if this is what he meant
Where to next?
The only thing left is for either GRRM to write the meaning of the name within one of the chapters of the story, or to discuss the name specifically in one of his myriad interviews, until then, this is all we have to go by.
But it's what I think that matters
Ok, my personal opinion on the matter is that the name Azor is GRRM's invented derivative of the word Azure. Azure, as defined by dictionary.com means:
1. of or having a light, purplish shade of blue, like that of a clear and unclouded sky.
2. Heraldry. of the tincture or color blue.
3. the blue of a clear or unclouded sky.
4. a light, purplish blue.
5. Heraldry. the tincture or color blue.
6. the clear, cloudless sky.
[possible spoilers for post season 5 and post-ADWD]
This can be tied into Jon Snow's character and storyline:
I have a strong feeling that this 'blue' character will 'clear the skies' and remove the fog which the Others bring with them