At the end of The Time of the Doctor, it is shown that Matt Smith has received an entire new regeneration cycle and using it he regenerates into Peter Capaldi. Capaldi's first question to Clara is about how to fly the TARDIS. Does this mean there has been a memory reset for the Doctor?
If so, has he forgotten his true name?
If he has forgotten his true name, then he can't bring back the Time Lords now can he?
The brain is muddled up as well as the body, and temporary amnesia is typical. It's a mild regeneration symptom, as they go. Other symptoms have included paranoia, violence, and coma.
Time for an updated answer after Series 8 and 9.
Even in the very first post-regeneration episode, when he's still (as @BESW puts it) a bit wacky, his memories of previous regenerations are still there, just a bit confused and hard to reach since he's only recently regenerated:
DOCTOR: SS Marie Antoinette. Out of control repair droids cannibalising human beings. I know that this is familiar, but I just can't seem to place it.
HALF-FACE MAN: How would you kill me?
DOCTOR: Sister ship of the Madame De Pompadour. No, not getting it.-- Deep Breath (Series 8 Episode 1)
This is a reference to The Girl in the Fireplace (Series 2 Episode 4), an adventure the Doctor had during his tenth regeneration.
In Into the Dalek (Series 8 Episode 2), he clearly knows and remembers what a Dalek is.
Similarly, in the Series 8 finale, he knows and remembers who the Master is and what Cybermen are.
Similarly, in The Magician's Apprentice (Series 9 Episode 1), he knows and remembers both Davros and the planet Skaro. We even see recordings of their previous encounters:
DAVROS: Then why are you here? Did you miss our conversations?
(Davros painfully throws a switch to start a series of clips on a small wall screen.)
DOCTOR 4 [Genesis of the Daleks]: If you had created a virus in your laboratory ...
DOCTOR 5 [Resurrection of the Daleks]: I'm not here as your prisoner, Davros ...
DOCTOR 7 [Remembrance of the Daleks]: Unimaginable power! Unlimited rice pudding!
DOCTOR 10 [Stolen Earth]: Everything we saw. Everything we lost.
DOCTOR 6 [Revelation of the Daleks]: But did you bother to tell anyone they might be eating their own relatives?
DOCTOR: Yes, yes, yes, okay, you've made your point.
DAVROS: Have I?
DOCTOR 4 [on screen]: If someone who knew the future pointed out a child to you, and told you that that child would grow up totally evil, to be a ruthless dictator who would destroy millions of lives, could you then kill that child?
(The Doctor turns off the recordings.)
DOCTOR: I get the point.-- The Magician's Apprentice (Series 9 Episode 1)
In The Girl Who Died (Series 9 Episode 5), he remembers a specific event from his tenth regeneration:
CLARA: Doctor, what's wrong with your face?
DOCTOR: I think I know why I chose it.
DOCTOR [memory]: It's like I'm trying to tell myself something.
DOCTOR: I think I know what I'm trying to say.
DONNA [memory]: (to Doctor 10) Just someone. Not the whole town. Just save someone.
DOCTOR 10 [memory]: Come with me.
DOCTOR: I know where I got this face, and I know what it's for.-- The Girl Who Died (Series 9 Episode 5)
In The Zygon Invasion/Inversion (Series 9 Episodes 7-8), he remembers the Time War and the events of the 50th anniversary special The Day of the Doctor:
DOCTOR: There are safeguards beyond safeguards. I did this on a very important day for me and this ceasefire will stand. [...] I don't understand? Are you kidding? Me? Of course I understand. I mean, do you call this a war? This funny little thing? This is not a war! I fought in a bigger war than you will ever know. I did worse things than you could ever imagine. And when I close my eyes I hear more screams than anyone could ever be able to count! And do you know what you do with all that pain? Shall I tell you where you put it? You hold it tight till it burns your hand, and you say this. No one else will ever have to live like this. No one else will have to feel this pain. Not on my watch!
-- The Zygon Inversion (Series 9 Episode 8)
In the Series 9 finale, he has retained many of his memories of Gallifrey, including the barn where he grew up, the Cloisters, Rassilon and how to deal with him, and most importantly how he stole the TARDIS way back in his first regeneration:
DOCTOR: A long time ago, there was a student at the Academy. He got in here, disappeared for four days. Showed up in a completely different part of the city. Said the Sliders talked to him, they showed him the secret passage out. And we just need the code.
CLARA: What, and the kid told you the secret?
DOCTOR: Ah, no, he didn't tell anyone anything. He went completely mad. Never right in the head again, so they say.
CLARA: Okay, that's encouraging.
DOCTOR: The last I heard, he stole the moon and the President's wife.-- Hell Bent (Series 9 Episode 12)
He also remembers a previous adventure with Amy and Rory, from his eleventh regeneration:
DOCTOR: I think that we were here, you know? I think that we were here together once. I'm sure I'll remember. Over here.
(The tables by the wall.)
DOCTOR: Stupid Doctor. Amy and Rory. It was Amy and Rory.-- Hell Bent (Series 9 Episode 12)
Finally, in the most recent episode (the 2015 Christmas special), he instantly recognises River and the fact that they were married, and of course her pet catchphrase:
DOCTOR: Do I know you?
RIVER: You most certainly do not.
(She throws back the hood. The Doctor smiles broadly.)
RIVER: And now that you've met me, you'll do your very best to forget me.
DOCTOR: River!
NARDOLE: Oi! Doctor Song to you. Sometimes Professor, but mainly Doctor.
RIVER: Don't use my name. Ever. How do you know me?
DOCTOR: Well, it's a tiny bit complicated. People usually need a flowchart.
RIVER: It doesn't matter. If either of you use my name again, I will remove your organs in alphabetical order. Any questions?
DOCTOR: Which alphabet? (grin fades) Sorry, you really didn't want these questions, did you?
RIVER: This way. We don't have a lot of time.
(She leads the way into the saucer.)
DOCTOR: What seems to be the problem?
RIVER: My husband.
DOCTOR: Your husband?
RIVER: Didn't you read my message? My husband, yes. My husband is dying.
(The Doctor stands still.)
NARDOLE: Something wrong?
DOCTOR: I think I'm going to need a bigger flowchart.[...]
(She meets the Doctor's eyes. He smiles and the penny finally drops for her. Long pause.)
DOCTOR: (sotto) Hello, sweetie.-- The Husbands of River Song
So yes, he seems to remember everything from his previous regenerations.
He hasn't reset his memory. He is just in the post-regeneration craziness. He'll snap out of it once he gets used to the new body. Also remember, 11 walked right into a tree after his regeneration. So we're not far off I'd say!
So what happened here I believe that when he was "reset" that meant that he is technically the first Doctor in the new regeneration cycle. Timelords are not normally supposed to have more than one regeneration cycle so it is very likely that he is suffering from some sort of amnesia. Also Capaldi will in the future be able to pilot The Tardis as shown in the Day of the Doctor.
