A thesaurus can give some answers and one word alternatives (synonyms) for close in the context of closing an object would be
bang, bar, block, bolt, button, caulk, choke, clap, clench, clog,
confine, congest, cork, dam, exclude, fasten, fill, lock, occlude,
plug, retard, screen, secure, shut, shutter, slam, stopper, and stuff
Antonyms are opposite to synonyms and as you will have found, antonyms in this context would be referring to opening an object.
Now we need to narrow the synonyms down for context when referring to closing a door. These would be
bang, secure, shut, and slam
Now as a native speaker, I would like to point out that, the use of secure can be used in this context, however it would more often refer to the locking of the door after it is closed.
I would understand "close the door" or "shut the door" to be generally in a reasonably quiet manner although closing and shutting can be done in a loud manner. If using close or shut you can always use the adverbs quietly or loudly to avoid confusion.
Please close the door quietly
If you use the words bang or slam they are definitely referring to a loud closing of the door.