I've been doing to much non dmck stuff and you have been quiet for too long.
Takagi is Matsuda au, what is Takagi/Matsuda's personality now that he has his memories back.
Which name does he use, his current name or his original name.
What is his relationship with everyone else now.
Sorry, most of my thoughts recently have been about the yokai AU so I haven't really been able to share them since the introduction post isn't done yet (in my defense, there's a lot of yokai XD. Megure in particular is giving me more trouble there than expected. There aren't really any Yokai with tired dad energy XD)
After he regains his memories in the Matsuda AU, his personality is kinda a mix between Takagi's and Matsuda's. He has more confidence than he did as just Takagi, but he isn't quite as confident as he was before the amnesia. He can be a bit more blunt at times, and he speaks his mind a bit more than he did as Takagi, (for example, his "and what generation is he from" comment about Conan would have been said out loud rather than just staying in his head like in canon. That episode is long before he regains his memories, It was just the best example I could think of) but he isn't as abrasive as pre-amnesia. And the traits Matsuda and Takagi both share remain as strong as ever.
I have mentioned this before, but how he acts can change depending on who he's with. When he's with Zero more of Matsuda comes out but when he's with Chiba more of Takagi comes out. Sato and Shiratori can both bring out more of either side depending on the situation.
His legal name stays as Wataru Takagi. It is really hard to change your name in Japan. You cannot change it simply because of personal preference, you need to prove that there would be negative consequences if you were to continue using your current name. When they changed it to Takagi they were able to argue that using the name Matsuda Jinpei would cause unnecessary pressure and distress for himself and others. (And even then the higher ups probably had to throw some weight around to get it approved.). However there wouldn't be any provable consequences to continuing to use the name Wataru Takagi after his memories return, so he wouldn't really have the option to change his name back to Matsuda.
As for what name people use for him, he mostly just tells people to use whichever name they're more comfortable with. Zero exclusively uses Matsuda. Most of the officers use Takagi. Shiratori, and a few of the other officers who knew Matsuda during that 1 week between his transfer and the explosion, tries to use Matsuda but often slips up and, as a result, ends up switching between using both names.
As for which name he personally prefers, he doesn't really have a preference for the family names, but with the given names he prefers Wataru because of the connection it has to date. It feels like he's got a piece of his friend with him. (Though it doesn't take a lot of soul searching before he realises either of these)
As for his relationships with everyone else, I think, beyond a brief period of awkwardness where everyone is still processing the information and unsure how to refer to him (something which is not helped by the fact that he is probably also having an identity crisis during this time), most of the relationships remain fairly the same.
I have talked about how Sato feels about the situation before and, at first, there is a bit of strain on their relationship as a result. Partially due to her tendency to try and bottle up her emotions, partially because this is something that's considerably harder to bring herself to share with Takagi. But things do get better when Takagi convinces her to talk to Yumi if she's struggling to talk with him, and he and Sato work through things as a team.