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I've noticed that both Dobby and Kreacher refer to themselves in third person, and got to thinking that it might be intentional of J. K. Rowling, to emphasize elves' depersonalization in the wizarding world. However, Harry is also referred to in third person (to his face) by Dobby, and Dobby continues to speak of himself in third person after he is liberated.
Dobby had difficulty dissing his previous masters even after he was free - meaning that full liberation starts with one gaining one's freedom but does not end with it.
House-elves were servants who were expected to be subservient.
The word "I" is a word of power - it is a means of taking ownership of one's feelings and thoughts.
"Maybe we should wait until after supper to have cookies"
is not as authoritative as saying
"I think we should wait until after supper to have cookies"
Dobby doesn't use the word "I" but I don't remember much use of the word "you" either.
"Maybe we can do something else"
is less authoritative than
"Will you stop doing that"
It may be forbidden for House-Elves to address themselves as "I" or address their masters as "you"
As far as each other, it would be a different matter - house elves take pride as to who their master is - having an inferior person act as if they are the house-elf's master is an act of shaming. Thus, for house-elves to use the words "I" and "you" would be to elevate themselves over other house-elves and would be a means of shaming each other.