So! Derp Rock Shooter and the DR and what happens next in the wake of the anime.
Who or what is she?: For a start she's not, strictly speaking, Mato. If anything she's a facet of Mato, representing her general force of will and a desire to be with Yomi. Trouble is, in the aftermath of the anime, she currently thinks she's Mato, or is at least extremely muddled and strongly identifying with her.
It goes something like this: BRS and Mato merge on up to do their business - kicking ass, taking names, and exorcising Dead Master (who, it seems fairly clear, is Yomi's possessiveness and jealousy) with the power of love and hugs. When they split, and Mato returns to her newly happy life to abuse Yuu and mack on Yomi, BRS remains in the hukeworld but... now feels terribly lacking and (see below re: DM and STR) suddenly alone. Here's this figment residing in an empty, bleak landscape where nothing happens but endless fighting, and thanks to Mato she's had happy childhood memories and thoughts and feelings shoved forcibly through her. She's torn; uncertain how to reconcile stoic badass and derpy dumbass and very much drawn to a happier and less crappy life.
Then she gets flung at the DR, and it's considerably less bleak and emo than her home dimension and even something like the normalcy she's been presented with, and she gets even more muddled and instead just decides to roll with it, taking the memories and identity she's been given and falling into them. As such she's BRS but with strong hints of Mato; she remembers the motions of how to have a happy normal life but they're only borrowed; she hasn't really experienced it first-hand or ever quite worked through it herself, hence the whole DRS awkwardness. A Mato turning up would cement her identity as BRS and not specifically Mato, but it can't knock free those feelings.
What about 'I killed my friend!', or DM and STR?: This is shakier, but bear with me. BRS identifies strongly with Mato, and as such strongly equates DM and Yomi as being the same person in much the same way. On top of that, if BRS and DM really represent and are affected by their respective people, then it's entirely possible that before everything went to hell they were allies, or at least as close as you get in the hukeworld; in the anime she never really gives off the feeling of wanting to kill DM, instead offering her hand again and again. But, by being far too stubborn and tsun for her own good, DM is killed off at BRS/Mato's hands, then Mato goes home and BRS is left with... nothing. No DM to be best buds with because she's dead, and even STR is out of the question as back in the real world Yuu is busy having a jealousy apocalypse, and so BRS is left feeling like she killed the closest thing to 'Yomi' she has and is now as alone as ever - or moreso, because now she feels it. Hence, baaaaww.
If they turned up, BRS would push the peace thing pretty hard. She likes the DR a lot mostly thanks to it not being a bleakass world of fighting, where she's learning better to interact with and be around people in a normal fashion, and she's hopeful that DM and STR could learn to know something other than the empty world they come from.
Other changes?:
- She's lost the normal sword, and just has the cannon. But that's okay because it can turn into the clunkiest, most stupid sword you've ever seen, or it can shoot regular balls of energy, or it can tear up an entire building by shotgunning 'rock bullets', which are basically big glowing blue rocks that explode. The fact that BRS and probably Mato consider this a cool name for them speaks volumes.
- The whole 'name' issue may need working out with those people she's shared it with and/or a Mato player. Some angst may ensue, but it's fun to note you can attribute her giving people her surname to being not quite up with the whole 'people' deal. That's my story and I'm sticking to it.
- The eye definitely doesn't need to be on fire all the time, it's just an indicator BRS is being more serious about things. I'm keeping the 'cannon appears out of nowhere thanks to burning eye-ness' thing for simplicity's sake.