At the beginning of the Reverie Arc, Luffy’s achievements were compiled, greatly inflating his infamy, which was already immense to begin with.
This includes his relationship as a sworn brother to both the late commander of the second division of the Whitebeard Pirates and the son of Gol D. Roger, Portgas D. Ace, and the Revolutionary Army Chief-of-staff, Sabo; the fleet that unofficially formed under him; the infiltration operation of Big Mom’s territory, Totto Land, where he defeated Sweet Commanders Charlotte Cracker and Charlotte Katakuri, attempted an assassination on Charlotte Linlin herself, destroying her castle (unintentionally), and created a prompt alliance with Germa 66, the Sun Pirates, and the Fire Tank Pirates before escaping after the assassination had failed.
Though his capabilities were slightly exaggerated by the press, his achievements were great enough for him to be unofficially titled the “Fifth Emperor of the Sea”.
So is Luffy officially the Fifth Yonko? Let’s see.
People become an Emperor when they are recognized to be an Emperor within the story. And this isn’t just a journalist(“Big News” Morgans) trying to sell his newspapers that decides it, but a general consensus within the population or players in One Piece. So if the World Government/Marines, the other Yonkos, the other pirates and the general population start recognizing you as a Yonko, you become a Yonko.
In Luffy’s case, many chapters later the only mention about being Emperor, it’s still only Morgans to recognize him as Emperor.
Blackbeard still said there are 4 Emperors of the sea, the World Government also doesn’t refer to Luffy as a Yonko, Big Mom calls Fake News on the article and Kaido clearly does not see him on the same level either.
Shanks also said that the time he would be meeting Luffy is getting closer (but suggesting it is not there yet). Furthermore, no other pirate or member of the population has referred to Luffy as an Emperor yet.
So in a nutshell, he would not be an Emperor because he is not considered to be one within the story. The criteria to be recognized are:
Luffy holds a lot of influence, and you could also argue his crew size is very good with the Grand Fleet, but he lacks the power and as of now just holds only one single island as his territory. In comparison, Blackbeard was the one who got credit for killing Yonko Whitebeard, he overtook all of Whitebeard’s territories throughout the timeskip as well as Pirate Island, he defeated the remnant of the Yonko crew soundly and then become a Yonko within the frame of 1-2 years during the timeskip.
Currently Luffy is not an Emperor. It is possible that he will leave Wano on that status, especially considering that 1-2 Emperors (Kaido/Big Mom) might fall during the arc. This is set to be the longest arc in One Piece so a lot can happen.
*Theory by Dr_Dankology