I'm trying to deal with the names of the parts of a sentence
In the sentence : " I'm reading a book in the park".
I - subject
am reading - predicate
book - direct object
and... in the park. what is the name for this part of a sentence?

Question

Answer

"in the park" is a prepositional phrase.

Terminology for parts of speech varies (e.g. predicate has two competing meanings - you chose one of them) so if you are following a specific course, it would be important to stick to its terminology.