What is a collection of poems called when the poems are by one poet?
An anthologyis a word that is usually used for a collection of literature usually with a theme but with several different authors.
However, an anthology also can be defined as a collection of poems, short stories, and plays, which can be a single author collection or a group of authors collection.
The phrase "collected poems" is used as a reference to a group of poetry that one poet has written and published together. For example, a title of a book might look as this one does:
The Collected Poem of Emily Dickinson
Another possibility is the word omnibus. A lesser known meaning of the word is a collection of literature on a related subject or an anthology of the works of a single author.
It is also called an omnibus volume which is a collection of works by one author or several works on a similar topic, reprinted in one volume.
For example, a sentence might read:
I purchased a volume of the Jane Austen Omnibus which includes all of her novels.
The word discography is also defined as publishing the entire works of one author, or composer like a music artists' collection on a record or tape.
A very popular common name for a book of poetry or other miscellaneous writings by the same author is chapbook. This is an old word, but it is has come into wide usage in modern times, especially among poets who are publishing their own works. There are various articles to be found on chapbooks in Google. One of them is provided in the reference link below. According to this article by Brian A. Klems in Writer's Digest:
A chapbook is a small collection of poetry, generally no more than 40 pages, that often centers on a specific theme, such as exotic foods or wild animals or Justin Bieber. It’s typically saddle-stitched (like a pamphlet or magazine) and is a format well suited to smaller print-runs.
As Klems correctly states in his article:
As difficult as it is to sell fiction to a publisher, it’s even harder to sell poetry. Producing a chapbook is an excellent way to give audiences a sampling of your writing and potentially sell your work for a nice little profit.
It is extremely difficult for a poet to sell a book of his or her own poems to a publisher because there isn't enough money to be made from books of poetry. This, of course, is especially true if the poet is not well know. The idea of compiling a chapbook seems like an excellent one to me. The poet can begin by collecting her or her best works in manuscript form. There are more and more ways to self-publish books these days and many of them are very inexpensive. Obviously some research should be done in an effort to find the best publishers. It is a very good idea to go to big bookstores and look at some of the poetry books that have been published.
Klems offers some good advice. The book should be attractive and type-free. It should not contain much more than forty pages. They should have a general theme, if possible. Some bookstores will handle such books on consignment. With the enormous increase in the numbers of creative writers, due mainly to the fact that so many schools are offering courses and even advanced degrees in creative writing, a poet who aspires to gain an audience has to give attention to marketing his or her work in addition to creating it. Self-publishing seems to be the wave of the future--but look out for the kinds of vanity publishers who simply want to exploit writers with false promises and false encouragement.
I think the word you were looking for is CHAPBOOK. It is a valuable word to know these days. A lot of writers are compiling their own small chapbooks and sending them around to publishers as a form of introduction. Google has many entries about chapbooks.