Of these words, title should be the most commonly encountered. As you have observed, it refers to the identifying name given to something, such as a document or a work of art.
Title can also be used as a verb, as in
a report titled The Lost Land
Designate typically means assigning someone to a certain position, or marking out something to possess a certain quality, as in
the Wye Valley is designated an area of outstanding natural beauty
and
certain schools are designated ‘science schools’
The noun designation either refers to the act of designating something or to the label that has been designated to something, such as the above ‘science schools’.
Appellation is rather formal, and not commonly used. It simply refers to the name or title given to something. As far as I can tell, there isn't a verb form of this word.
It is also specifically used when discussing wines, to refer to the name of the region of origin of the wine. Wikipedia has more detail.
Denominate is also formal, and also means to name something. However, there is an implication that the term used to refer to said something is not the proper name that most people use to refer to it, instead being a term closely associated to the usual name.
While title has quite distinct a meaning, the other words are largely interchangeable in text. For what subtle difference:
Designate usually applies labels to things instead of naming them directly, and tends to imply that the labelling is official.
Denominate suggests that the name being given is not one that is commonly used.
Appellation is uncommon and may seem awkward in everyday use.
