Zarema is a modern Russian name. No meaning was given for it at the Russian language baby names site I found it at; as far as I can tell from further searching, it’s of Chechen origin. The one site which gave a meaning said it may mean “sweet water” or “war maid.” This name is also possibly derived from the Persian name Zareen, meaning “golden.”
I personally tread very carefully when taking any name site besides Behind the Name as an accurate source for name meanings. It’s all about vetting your sources. I’ve found out a lot of names don’t have the meanings I was led to believe they had. Honestly, a lot of name sites are garbage, the way they lump names in categories they clearly aren’t part of, and by giving blatantly untrue meanings and etymologies. Zarema is obviously a very real name, but I’m not going to definitively give it a meaning or etymology in the absence of scholarly sources.
Zoriy is a modern Russian name, not an invented Soviet name. It means “morning” in the adjectival form. Russian is such an amazingly rich language, with so many forms of words branching off from one simple root. One of the basic nickname forms would be Zorik.
Sources consulted:
http://panzercentral.com/forum/viewtopic.php?f=96&t=36301 (penultimate post)
http://www.namenerds.com/uucn/listofweek/soviet.html
http://horo.mail.ru/namesecret/
http://www.devichnik.ru/9810/imia.html (male)
Onomastics Outside the Box 
I’ve never though abut it but Morning would make a lovely name – if it didn’t actually sound the way it does. There is Dawn, but Morning has a lovely meaning as well so Zoriy, or Zorik, would be a good substitute, especially as they are classed as ‘real’ names.
Very interesting! I’ll have to bookmark Behind the Name because I use naming sites for my writing–and also have had a fascination with names prior to writing fiction. I agree, many of the sites are garbage (and an assault to the eyes).
So glad I found your blog for the A to Z challenge! My posts are about Memorable Characters.
If you’re worried about unreliable websites when it comes to onomastics, then you should be quite wary of Behind the Name; it’s derivations and etymologies are often suspect, and it cites no sources.
I always get frustrated with name sites. My go-to method has been to go to 20000-names.com, find a name based on meaning, and then try to check in other places to see if it’s correct. I might ask for help next time 🙂
Great theme and great blog for A to Z! I really enjoyed visiting. Congrats on finishing the challenge 🙂
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