In Shrek when Donkey asks Shrek his name, Shrek pauses before giving it: "Eh ... Shrek".
He does this again when Princess Fiona asks his name.
Anyone know why?
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The film's draft screenplay offers an answer to both instances. I've copied directly from the script itself with the original stage direction placed in [square brackets].
Shrek is taken aback that Donkey isn't scared of him. This seems to be the first time this has happened for some considerable time and the script describes him as "disarmed" and "surprised" by Donkey's exuberantly friendly attitude. His hesitation seems to simply be an extension of this bafflement and mild surprise at the (non sequitur) question.
SHREK: NO! I'm an ogre! You know - 'grab your torch and pitch forks'! Doesn't that bother you?
SHREK: [a little surprised] Really?
DONKEY: Really, really.
[Shrek is suddenly disarmed.]
DONKEY: Man — I like you, what's your name?
SHREK: [hesitant] Ahh ...Shrek.
[Shrek turns and continues on his way]
When Fiona asks the question, Shrek is described in the script as being "preoccupied". He's clearly trying to decide which way is best to go to avoid the man-(and ogre-)eating dragon he just evaded and is no mood for an extended chat. Again, the question seems to catch him slightly off guard.
FIONA: [fed up] Well, can I at least know the name of my champion?
[Shrek is preoccupied trying to figure which way to go.]
This ties in nicely with the description in the film's official novelisation
"Well, can I at least know the name of my champion?" asked Fiona, thoroughly fed up. "Umm . . . Shrek," said the ogre, who was preoccupied with trying to figure which way was out.
I believe it is because since he is an ogre, he is not used to conversation.
People usually grab their torches and pitchforks when they first see him, he's never heard someone try to talk to him and ask him his name.
Therefore he is momentarily confused when someone asks his name, because he is not used to people approaching him like that, and also as dmckee added below, "he's not used to needing to remember a label for himself"
From this site: (bolding mine)
Shrek: Listen, little donkey. Take a look at me, what am I?
Donkey: Uh... [looks Shrek up and down] really tall?
Shrek: No, I'm an ogre! You know, "Grab your torch and pitchforks!" Doesn't that bother you?
Donkey: [shakes his head happily] Nope.
Shrek: [surprised] Really?
Donkey: Really really.
The most likely reason would be because he thinks it is strange that someone would ask him that. As hammythepig said, people usually grab their torches - meaning that Shrek is a very lonely person who has no one to talk to because everyone feared him.
Since Donkey was the only one who wasn't afraid of Shrek, Donkey was the only one to ask him the question (since everyone was afraid of Shrek). Since Shrek never had anyone to talk to before (he wasn't social), he probably was deciding if he should answer, resulting in the pause before answering.
As you see in Shrek, he has no friends or any social encounters with anybody. Then in the last movie, you see that Shrek thought he was the only ogre left. That would mean that he was all alone for quite some time.