I'm gonna come in here and give these group of characters some leeway here (Pablo Kelly and Brandy), they only got like 2 seasons worth of actual development/actual arcs for their characters in a half hour format and we're stuck spinning their wheels in the second season because for some reason Craig and the writers for S2 decided they wanted to focus on dude bro/gross out humor for most of that abysmal season's story instead of focusing on what they set up in S1 which really killed Pablo and Kelly's momentum as characters and the whole situation with Kelly being almost positioned into being Ash's daughter by the end of it in the original finale's story. (Can't believe i'm saying this, but thank god Rob Tapert put the kibosh on that nonsense even if he had to drive a freaking train through S2's "story" up to that point with that put together last minute S2 finale, and we we're spared that original S3 story and we got a much more competent showrunner in there and gave us probably the show's best season, because *gasp* they actually focused on the characters and gave them all plenty of stuff to finally chew on in fleshing them out and wrapping up the threads established in s1.), those two finally got to start doing interesting stuff in S3, got good character development that should've happened after s1. Hell, Brandy only got 1 season of development and barely got to come into her own towards the end of it when it really felt like we were just starting to see that character start to bloom.
To me personally, i'd love to see those three again in their own little sphere in some type of 5 episode mini series or just a film that show cases what they got up to after Ash went under in hibernation with the right creative team behind it.
It would be nice to seem them given proper arc's and fleshed out properly in a longer but breezy run time beyond what we got in the show, hell i'd love to see more of what Pablo could do with his new found gifts S3 bestowed on him, the possibilities there are pretty creative in what could be possible with what they left on the table with him playing the double agent/undercover/el brujo especial role.
It would be dope to see Kelly develop more past her anger/grief and become what they set her up as in the s3 finale, it really felt like they finally got her past just wanting to be the "next ash" (with ash rightfully calling that shit out, which now thinking about it, feels like the writers taking a pot shot at the writing team of s2 and Craig for that story they we're setting up.) and come into her own. Now in hindsight, Kelly was the character that really got shafted in s2 after what was set up in s1. Same thing with her as well as Brandy which i'm about to talk about here, Kelly was finally starting to bloom in to her own character with more interesting things to do beyond what S2 was positioning her to be and, we didn't even get to see that, damn shame cause Dana plays the character well and she deserved better from the writers going into s2.
On to Brandy. Brandy really came into her own as well as a character towards the end of s3 but like Kelly, her journey ended before it even got going.
her character once she got over the hurdle of believing her father and was fully on their side after the events at the prom, all of her scenes with Ash towards the end of S3 and the sequences she was given to carry really sold me on her a lot and it's a damn shame she only got 1 season, she should've been there from the start with Kelly and Pablo, i wanna see her come back as a more experienced fighter and we get to see more of her dynamic with Kelly and Pablo fleshed out, i really liked her dynamic with Kelly specifically when the two were together fending off Pablo.
As for the Ghostbeaters name, it was established in s1 Ash and Kelly both didn't like that name , but i'm gonna guess in character wise, they didn't wanna harp on Pablo about it too much cause well, he was just eyeballing the name and was just wanting to give them a fun team name in the moment. So i have to imagine they kept on using it as a little endearing "in-joke" between the three of them to put a name on their bond as a team, all three know the name is lame and cheesy but it's a core memory of when they officially got together as a team to take on evil and that's probably why it stuck around.
Any ways, to leave off this big rambling/defense post, i think Pablo, Kelly and Brandy deserve to have their own story to tell that properly realizes the potential s3 left them on with a good writing team behind them that pushes them all forward as characters beyond what the original run of the show gave them, but that's just my two cents.
I do agree with you Sutur that Kelly, Pablo and Brandy would not be a good fit for this current "Deadite/Book" saga we are currently in with the franchise at the moment and like i mentioned above, their continuation should take place in their own sphere that matches up with the AvED timeline without the need to bring Ash into it and let those three lead the story.
Give us that apocalyptic story we've been dying to see for years with those three having to carry that weight and struggle with Ash out of the picture during that time frame and show us how it got to that point where Ash wakes up in that futuristic world and how Pablo, Kelly and Brandy played a part in achieving that, to me that's a interesting story to tell with the right tone which to me, you have to bring in a serious tone with how dire that situation is which they did a splendid job of doing in S3 and it turned out great!