The notion of someone signing up isn't super weird necessarily, the prologue is very strange though once you take into context the idea that they did it willingly. Kaede and Rentaro slowly figure it out, but it didn't look like they were filled with excitement, and it seems strange that of these 16 people who are such super fans and ready to throw their lives away for this show, only Rentaro is the one to figure out immediately that it's a killing game because of the amount of people and the setting. I feel like super fans would all have had that thought go through their mind instantly upon seeing the situation.
For real. The moment the Monokubs show up, that should've tipped everyone off immediately. Even if you want to argue they're not actually the real "Monokuma", they obviously look like him enough to the point that everyone should've responded immediately if they were alleged fans. Kaito even reacts to the Monokubs with total confusion. And yet, according to Tsumugi, they only conveniently respond once they're given their Ultimate outfits.
Another possibility is that Danganronpa might not be as big of a show as Tsumugi likes to pretend it is and is just something several characters may have heard of but never actually bothered watching/researching into.
Also if we're going to subscribe to occam's razor, then Kaede and Shuichi introducing themselves with their real names in the prologue is straight up a plot hole. No real point in bringing it up.
Not quite. Kaede basically forces Shuichi to say his name just so she can give him a "get a hold of yourself" talking down. The fact that we actually find out their names (and also see how different their personalities are before their shift to Ultimates, with Kaede being forceful/realistic and Shuichi being more prone to panic and reflexive) but no one else's in that prologue is a deliberate detail about what it's meant to be.
Because they're in the game by that point.
According to Monokid, they're not. It's even pointed out that Monophanie was supposed to alter their memories but didn't. And even if they were, what's the point of telling us that they responded with glee once they got their outfits? If the purpose was to make them forget everything but also put them in a situation where they somehow remember that they signed up/were fans, that's a plot hole.