Why is Moshe name not mentioned in this weeks Parsha, T'tzave?
Me'or Einayim points out that Tetzaveh is (nearly) always read immediately before or after the seventh of Adar, which is Moshe's (birthday and) yahrtzeit. So his name is missing from this parshah specifically, in mourning for our loss.
On a more positive note, there is a long talk by the Lubavitcher Rebbe zt"l (Likkutei Sichos, vol. 21, pp. 173ff; adapted into English at Chabad.org) in which he points out that in a sense Moshe is present even more in this parshah than usual. Its very first word, ואתה, "and you," expresses his existence even more strongly than the use of his name.
He then goes on to explain what Moshe was trying to accomplish with his "threat." He was demanding that G-d be willing to re-establish His relationship with the Jewish People on an essential level that transcends Torah, and that if He wouldn't be willing to do so, then Moshe was prepared to forfeit his place in the Torah in favor of retaining his connection with his people. Thus,
Baal HaTurim says that since Moshe said "Mecheini Na M'Sifrecha Asher Kosavto" in Parshas Ki Sisa. The question remains why in Parshas Tetzave is there no mention of Moshe. HaRav Shaul M'Vilna answers since Moshe said Asher Kosavta which is a Lashon Avar - past tense - therefore it was omitted in Parshas Tetzave. Another reason is that the Gematria of Asher is 501 which is also the Gematria of Tetzave.
The Gra says that since most years Zayin Adar - 7 Adar comes out in Parshas Tetzave - Hashem who knows what is going to happen left his name out of this Parsha.
In the Sefer Panayach Raza he mentions that since Moshe was originally supposed to be the Kohain Gadol, however he lost it due to saying "Shelach Na BeYad Tishlach" therefore in Parshas Tetzave which talks about the Bigdei Kehuna he is not mentioned.
Source for all the above: Torah L'Daas Chelek 1
I do remember hearing that the reason is that Hashem did not want to erase Moshe's name, however since he requested it Hashem kept pushing it off until there was no more pushing it off, and therefore it is not mentioned in Parshas Tetzave.
On a peshat level:
A parsha (actually a sidra) is the portion set up to read in a particular Shabbat, as set up in Bavel. In Eretz Yisrael, they had a different division, of a third the size (called a parsha).
I would therefore assume that in Eretz Yisrael, there were a good many "parshiyot" that did not have Moshe's name, and so, Tetzaveh was in no way unique. (Aside from the fact that Moshe was not mentioned at all in sefer Bereishit.)
The reason Moshe does not appear in this parsha has to do
Of course, this creates an interesting phenomenon which can be used for the sake of derash of derush. And the other answers here cover that. The question, however, assumes that there must be something meaningful about Moshe's absence, and so I think it a good idea to point out that this is an assumption.