Yup, I'd call and ask for the name also.

I would never start a letter with Greetings. Sounds very telephone-solicitationish.

Any letter that starts with Greetings, I probably wouldnt read either. Id assume it would be from somebody trying to sell me something that I didnt ask for and if they cant bother to take two minutes to get my name, then they are probably not somebody Id want to deal with anyway. If two minutes out of their life is too much for them to handle, where will they be when I have a problem that has to be resolved thatll take more time than that.

The only Greetings that is acceptable is one that comes at the top of a Christmas card or Christmas letter from a friend or family member who is addressing your whole family because it would be ridiculous to name all of them.