From a process standpoint, merge-request is probably more accurate, but I've always thought pull-request captured the hearts and minds of developers because it better represents how the requester feels about the request.
"Pull request" communicates "I just did a bunch of work, please recognize it and me." "Merge request" communicates "I just did something that is going to make your life hard, please do a bunch of work on my behalf." The later may be more accurate but the former is more emotionally satisfying to the dev making the request.
"Pull request" communicates "I just did a bunch of work, please recognize it and me." "Merge request" communicates "I just did something that is going to make your life hard, please do a bunch of work on my behalf." The later may be more accurate but the former is more emotionally satisfying to the dev making the request.
Edit: reducing verbosity