Hi Menrov,
One possibility, just guessing of course, is that Jesus spoke of himself in the third person due to his prayer having an audience (those present at the last supper). At verse 4 he does pick up speaking in the first person.
In other places Jesus also uses this third person reference to himself. (E.G. Mt 25:31-46) Moses often records himself in the third person in the Torah (assuming, of course, that he is the writer).
Another possibility is that the writer of the gospel account begins his recording of the prayer with Jesus using the third person self-reference as an editorial choice for the sake of people who would be reading the account later. Perhaps this was a normal way of recording historical events. But all the gospel accounts have Jesus speaking of himself in the 3rd person. So it seems to me more probable that this was Jesus own method of referring to himself.
There is an interesting StackExchange discussion of this topic here. (Although, admittedly, the StackExchange discussion goes on to center around the "Son of Man" title from Daniel 7:13, 14. And here is a short PDF on this topic. And here is another web-page on the topic.
In Jn 17:1 Jesus uses the 3rd person noun ("your son"), in verse 2 the 3rd person pronoun ("him"), in verse 3 a 3rd person name/title ("Jesus Christ"), and then picks up the 1st person self-reference in verse 4 ("me"/"I"). Perhaps there was some purpose in stringing those things together in that order.
