My dad once asked me "why do Internet creators call themselves influencers, isn't that a sinister thing to call yourself?"
No one ever chose to call themselves that, this definition of the word was abruptly inserted into the English language, back in 2016 according to Google Trends.
Articles purporting to cover the word's history will apply it's current definition retroactively, back to celebrity fashion of the '80s, Josiah Wedgwood, or Shakespeare. This isn't an answer, it's high school essay filler. Quora users parrot these answers. These articles were all written within the last 3 years and are likely copy-pasted from each other, but incidentally I notice this is a problem on Wikipedia in general - no distinction is made between when something first appeared and when it actually got popular.
Looking through 2016 articles, one puts the word "influencer" in quotes, another calls it a buzzword. It's possible that it started as a business term, cynically categorizing people as potential money-generating statistics. A 2019 Medium article cites a 2018 New York Times article for giving us the term "nanoinfluencer." I had always assumed that old media invented the new definition around the time they started seeing Internet creators as a threat. Remember that 2017 was the year of the "adpocalypse" on YouTube.
Old media are never called influencers, of course.