I searched on the Internet about poem recitation, and what came up was poetry recitation or poem recital.
Which is more grammatically correct?
A recital is a performance of a selection of pieces, usually music, however the term poetry recital is used.
Some artistic events might have both poetry and pieces of music. In such an event person might recite a poem. Note that strictly "recite" implies that the poem has been memorised, the performance is from memory.
These days it seems that when a poet delivers their poems to an audience they may not do so from memory, and so perhaps that is why the term
seems most common.
I would not use Poem Recital unless the intention is to say that single poem is being delivered. The cases I've seen for using this term are to describe such single performances on YouTube.
Another way of saying that is to use the noun recitation: they gave a recitation. There is something rather artificial about the word recitation. Back in the early 20th century in the UK there were Music Halls, where a combination of singing, dancing, comedy, ventriloquism and other light entertainment was given. One such item might be a monologue, often of a poem by Marriot Edgar. The artist might introduce the item using a fake upper class accent:
H'and now H'I shall given a short reeeciiitashun entitled "Albert and t'Lion"