Some types of letters — i.e., messages that you write on a piece of paper and send to someone — have their own name.
In fact, for example, we call 'note' a short letter to someone, 'rejection' a letter that tells you that you did not get a job or were not accepted by a school, 'response' a reply to any question or letter, and so on.
Even a letter sent regularly to members of an organization, containing news, has a name, 'newsletter', which is, as in the cases already mentioned, a single word.
That being said, my question is, is there a single word which one can use to refer to a 'love letter' — i.e., 'a letter telling someone how much you love them'?