"Letter of request" sounds more proper. "Letter of recommendation" is what I always see and use, and as for "letter of complaint", it also sounds better than "complaint letter". Most times, I suppose you would use "Letter of..." rather than "... letter"

Before everything I have to say you can simply search your question on google! as I do and If you couldn't find your answer you can get help from your friends on italki, here're sample links of many: http://www2.elc.polyu.edu.hk/cill/eiw/complaint_letter_constructor.htm http://oxforddictionaries.com/words/letters-of-complaint Then it shows you can use both types, but the 2nd one is common.

I think the 2nd one

"Letter of recommendation" is the only one of those I've heard used. "Recommendation letter" sounds weird and off. I've never heard anybody say in my 16 years of living "Letter of complain" nor "complain letter". One would simply say "complaint" the fact that it is a letter is understood through context. This at least my experience. By the way I'm from USA, if that helps.