“More importantly, who says that that is what they meant? Rashi DOES NOT explain it that way. He writes כל אחד היה דורש אחר שמו. Why doesn’t he simply say that they said their Rebbe was Mashiach?”
1. there are various people over the past few hundred years who interpret that gemara as referring to who moshiach is. It shows a lack of knowledge to say that there is no such thing as that interpretation outside lubavitch.
2. a reverse question: if rashi just wanted to teach what the names of moshiach are why didnt the gemara and rashi just say these are the names of moshiach? Why does the gemara say each house said a specific name, and why does rashi add that each rebbe darshined his own name like that of moshiach? Why would he connect his name with moshiachs name? Why didnt he just teach what moshiachs name was independent of his own? Dont you find that strange that he said moshiachs name was basically the same as his? Why connect it to his own name? Dont just cut off the question at an artifical point and say well he darshened but he just did it to darshen.
ultimately, Pashut pshat is because he was teaching he could be moshiach and they accepted. I dont need to prove whats straightforward, whats pashut is pashut, and one should go with how things sound unless one has reason not to.
2b. a proof to what im saying that these are not separate things can be shown from rabbi akiva and bar kochba. It says rabbi akiva darshened on bar kochba the verse “a star(cochav) will shoot forth from yaakov”. Here we see rabbi akiva darshoned on him as a RESULT of his thinking bar cochba was moshiach. So ones immediate response to darshening pesukim about moshiachs name after a rebbe aside from having obvious implications, already have a clear outright source that darshening means to believe the guy is moshiach. I didnt connect the two. Shas did. Now you want me to disconnect them for no reason and say we are making disinformation?