snip
The Kage most likely did something like that, literally announcing to the entire village as to who the jinchuuriki of x bijuu was. Surely they had a right to know who their 'hero' or 'scapegoat' was in the series, right? Because they were viewed early on as weapons which depending on how well villages were able to contain their prejudices, wind up leading to the defection or alienation of them. hence it wasn't really farfetched for outsiders such as the Akatsuki to locate the jinchuuriki when people were willing to let loose information able those monsters in humans forms wandering somewhere in the land.
But yes, it is undeniable that someone will be after the bijuu in your possession. If only of course they had knowledge of whether or not you well and truly had it in the first place. Fact is, SL doesn't follow the series
that closely, we don't hold as much animosity or value towards jinchuuriki (as in the series) and rarely ever discuss it in-character on a wide-scale. While I suppose it is logical for extremely keen sensors to detect who is a jinchuuriki (and perhaps jinchuuriki being able to detect other jinchuuriki, perhaps not very accurately but still gain a lead), hunters should still be forced to gather information should they possess neither of these perks.
Besides, knowing who the jinchuuriki of x bijuu doesn't automatically let you discover where they may be. If nobody knows or refuses to tell the truth regardless of the circumstances, and the hunter lacks techniques (or other means) to force the truth out of them, then they'd be forced to locate information and leads the hard way.
So anyway, I believe that unless the Kage were blunder-heads and didn't keep the jinchuuriki's creation confidential, as well as keeping a tight leash on those involved, then it shouldn't be public knowledge as to who is 'that' jinchuuriki until somebody spills the beans, or a freaky-keen sensor/jicnhuuriki detects them manually.