His father went to the school, but never graduated. It has never been clearly stated why that's the case, though it's implied it's related to him meeting Soma's mother; from this one might guess that "Yukihira" is his mother's last name. The failure to graduate may have hampered his renown, and lessened Tootsuki's desire to associate with him. Recall that the academy is set up as very punishing and almost militaristic, regarding those who fail to graduate as decidedly incapable of being a truly great chef. It runs counter to this belief to give a failure any recognition, and may actively encourage the institution to bury or at least ignore the connection.
Furthermore, Joichiro's professional career was characterized by constantly changing locations, and eventually hiding himself away in a local diner. That's not conducive to maintaining a strong presence in the culture; a few elites will know him, but before they can pass on the stories he simply moves away, leaving children no opportunity to learn except by happenstance (aka, Erina).
His change of last name was probably only known to a few people closest to him. Even Dojima took a long time to connect Soma to Jouichiro, mostly doing so by chance. As for why that monk seemed to know him by the Yukihira last name, and the timeline suggesting he also knew him before the name change, there are a few possible explanations, with my personal preference listed first:
- The author hadn't thought of this problem ahead of time. It only occurred to them later that a cook with his skills and connections should be well-known. This was at odds with the intent for Soma to be a darkhorse commoner, as the story was very early characterized as "local nobody struggles against the elites to becomes a big somebody, proving that passion and hard work are the keys to success". Ergo once the problem became inescapable, the author pulled the ol' "name change" maneuver, and intentionally drew as little attention as possible to the possible discrepancies with the early story. This is a common writing technique for serialized media. Manga, comics, anime, TV series, cartoons, etc. all tend to employ it of necessity.
- Essentially nobody knew that Yukihira Joichiro was the same person as Saiba Joichiro until just before the story started, when someone was able to find him and talk him into working for him around the world. Possibly this person was a long time confidant, and so did know these two people were the same, or maybe they just applied enough resources to find out what happened to Joichiro. Afterwards, now that he was back in the limelight he could now be recognized by former admirers, such as the monk, or word could otherwise slowly spread through patrons that connected the two together. Either way the monk can connect the two identities together, but the spread of information would have been too slow and localized to propagate all the way back to high school age students in Japan. Never mind the internet; we rarely even see academy students using smart phones or computers if they're not related to cooking something right then and there, and possibly with such elite and affluent customers even the internet is slow to pass the information along. Plus, as has been mentioned, lots of people have the last names Saiba and Yukihira, so there'd be little more than coincidence to connect Soma to Joichiro. It would actually be more unrealistic for people to assume a familial relation, even if they were aware of Joichiro's name change.
As a relevant sidenote, the headmaster of the academy (at the time the story starts), is later revealed to have been plotting something benevolent and that Jouichiro/Soma were integral to this plot. It was in the best interest of his plot that Soma be a complete unknown to the students, so he would have incentive to hide the Saiba/Yukihira connection.