In a way my understanding of why we don't use the name is for several possible reasons:
1) It would be a sign of disrespect if a mere mortal human would utter the name which represents the transcendental quality of our L-rd.
2) There is a mitzvah in the 10 sayings/commandments to not use the name of the L-rd in vain, or in a circumstance which is not befitting the holy/special nature of Hashems 'existence'. This is one reason why the Talmud explains that one should not use the word 'Shalom' in the bathroom because Shalom is a name of Hashem.
3) It is believed that the correct intonation of the ineffable name has actual physical and spiritual power, and those who possess this name are capable of wonders. An example of this is in the Torah when Moshe smote the Egyptian task master as it is said he did so uttering the name of Hashem. Heaven forbid the name should be used for ill purpose...
http://www.chayas.com/10plague.htm
3) In Moses’ initial contact with the Creator, he asked to know His Name. This seems strange, since the Midrash teaches that Moses knew the Divine Name, using it to kill the Egyptian taskmaster. Being a Levite, whose tribe faithfully preserved the holy traditions of the nation, how couldn’t Moses have known the Name of His G-d? Notice that HaShem did not then reveal to Moses the essence of His most sacred Name, but replies, “I Shall Be What I Shall Be.” Now E-hiyeh (I Shall Be) is indeed one of the seven holy Names of G-d that may not be erased. However, it may well have been a mild form of rebuke. Ancient magic and sorcery involved the use of various “holy names” in incantations to cast spells and manipulate supernatural powers. This practice is alive and well in India, as well as in largely extinct schools of pseudo-Kabbalah (as opposed to genuine Qabbalah). Considering Moses’ upbringing, his question could hint to the magical perspective of the ancient world, in which Moses was raised and educated. (Moses is not a flat character, but one who grows and develops, which could warrant a special essay in itself!) It is not inconceivable that at this initial encounter with the Almighty, he requested a holy name through which he might be expected to perform HaShem's wonders.
See also:
http://www.torah.org/learning/rambam/kriatshema/ks3.5.html
The Gemara in Shabbat takes note of the inclusion of *She'ilat Shalom* among those things which are forbidden in a bathhouse, and infers:
"...this supports R. Hamnuna's teaching in the name of 'Ulla, who said: It is forbidden to "give *Shalom*" to a fellow in a bathhouse, since it says: "[Then Gideon built an altar there to Hashem,] and called it, Hashem is peace (*Hashem Shalom*)..." (Shoftim [Judges] 6:24). If so, it should also be forbidden to mention "faith" in a Beit haKissei [note the seamless shift from bathhouse to outhouse], as it says: "[Know therefore that Hashem your God is God,] the faithful God [who maintains covenant loyalty with those who love him and keep his commandments, to a thousand generations] (Devarim [Deuteronomy] 7:9). And if you say, that is also true (that it is forbidden to mention "faith" there), but Rava b. Mahs'ya said in the name of R. Hamma b. Guria in the name of Rav: It is permissible to mention "faith" in a Beit haKissei! There [in the case of "faith"], the Name is not itself called that, as we translate: "The God of faith"; here [in the case of "Shalom"], the Name itself is called Shalom, as it says: "and he called it, Hashem Shalom."
In this discussion, we are introduced to the distinction between a "Name" for God and an "Adjective" for God. Since Gid'on called his altar "Hashem Shalom", we understand this to mean that "Shalom" is another name for God. Conversely, although God is described in the Torah as a "Faithful God", this doesn't imply that "Faithful" is a Name; rather, it is an altogether appropriate adjective for Him. The upshot of this is that if we identify a Name for God, that may not be said in the bathroom; however, an adjective which is associated with God isn't included in that prohibition.
Tosafot (Shabbat 10b s.v. d'M'targ'minan) raises an objection to this distinction: Just as the Gemara justifies permitting "Faith" in the Beit haKissei because the verse is translated "the God of faith"; similarly, we translate the verse in Shoftim "the God who makes peace" - so "Shalom" is also a modifier and not a Name! Tosafot's answer is based upon the wording of Gid'on: "Hashem Shalom" - and, if Gid'on only meant to say "God is the one who makes peace", he would have said "Hashem Sh'lomo" (lit. "Hashem who is [the cause of] his peace"). Rosh (Teshuvot 3:15) offers a similar response. However, Tosafot first explains that Gid'on called God "Shalom" because He makes peace. The distinction between this and "faithful God" requires clarification. This will be addressed below in section III.
