This happens to me frequently. I'll say, "Oh you know that guy... uhh... I can't remember his name. But he starts with a 'Z'." You can remember part of the word but not the whole word.
Is there a term for this situation? What causes it?
This is called the Tip of the Tongue phenomenon.
People in a tip-of-the-tongue state can often recall one or more features of the target word, such as the first letter, its syllabic stress, and words similar in sound and/or meaning. Individuals report a feeling of being seized by the state, feeling something like mild anguish while searching for the word, and a sense of relief when the word is found.
It's a very common phenomenon, and it presents itself in several similar forms, as the Wikipedia description notes. Remembering just the first letter is a common form but not the only cue.
There are a couple of suggested causes, but generally the problem is failure to completely retrieve information you "know" is in fact there. The Wikipedia article has some information on the general theories.
Anomic aphasia, also known as dysnomia, nominal aphasia, and amnesic aphasia; is a severe problem with recalling words or names. Wikipedia is a good source of info on the subject. Severe cases sometimes are traced back to a blow and subsequent damage to the left side of the brain.