When Hashem appeared to Moshe at the burning bush in parshot shamot perek gimil why did he call Moshe's name twice? He could have just said "moshe" ONCE!
The Zohar (Bamidbar 138a and 187b) points out that this repetition is further unique in that the two "Moshe"s are not separated by a pesik (vertical line), unlike other repeated names in Tanach ["Avraham | Avraham" (Gen. 22:11), "Yaakov | Yaakov" (ibid. 46:2), "Shmuel | Shmuel" (I Sam. 3:10)].
This, says the Zohar, was because Moshe was perfect from birth (i.e., he was the same "Moshe" throughout his life), unlike the others who, at the time when Hashem called them, achieved something that they hadn't previously had.
In Shemos Rabbah 2:6 it lists a number of reasons:
Unlike the other nevi'im (prophets) that had their names repeated such as Avrohom (Bereishis 22:11), Yaakov (Bereishis 46:2) and Shmuel (Shmuel 1 3:10) where there is a p'sik, a pause in between - Moshe is repeated twice without a pause in between the name. This is compared to someone who is carrying a heavy load and he then calls out "ploni ploni help me unload this heavy burden" without even stopping for a moment - This is understood to mean that the repetition of the name without any pause shows how Hashem felt the pain of the enslaved Jewish people and called Moshe twice without stopping to ask him to come quickly to redeem them of their burden. (As explained using the Eitz Yosef)
The duplication of Moshe's name without a pause unlike with other prophets (as mentioned in #1) is to demonstrate that unlike other prophets who had a pause in their communication with G-d, Moshe never experienced any delay in his dialogue/interaction with Hashem.
Rabbi Shimon bar Yochai says that the name is repeated to show Hashem's love for Moshe and to also express a sense of urgency i.e. when you call out someone's name twice it really conveys the need for help (Eitz Yosef).
The double name is to show that just as Moshe taught us the Torah in Olam HaZeh, he will in the future teach it to us in Olam HaBah.
We often see throughout the Tanach that Hashem calls someones name twice. We learn from the Mafarshim that this means Hashem is saying, 'I love you-do not worry my next request is not a hard one.' Often the double name is followed by 'Hinneni", here I am, meaning that I will do your next request without even knowing what it is. This is what we see with Moshe at the burning bush. Hashem calls his name twice meaning I love you and Moshe responds Hinneni without knowing the request. As we continue the story Hashem's request is not an easy one and does not seem to follow the principles set out above. However, a careful reading of the text shows that Hashem's first request and the request to which the double name and the Hinneni refer to is in fact the removal of Moshe's shoes. Hashem continues, using Moshe's name only once when he requests that Moshe go down to Egypt to speak with Pharoh.