The Significance of the Name

In Jewish thought, a name is not an arbitrary designation or random combination of sounds. Names convey the nature and essence of the named.
In English, we often refer to a person's reputation as his "good name." The Jewish concept of a name is very similar to that idea.
In Ex. 3:13-22: Moses asks God what His "name" is. He is not asking "what should I call you;", he is asking "who are you; what are you like; what have you done." This is clear from G-d's response. G-d replies that He is eternal, that He is the G-d of our fathers, that He has seen our affliction and will redeem us from bondage.
Because the name represents the reputation of the one named, a name should be treated with respect. G-d's Names, in all of their forms, should be treated with enormous respect and reverence.

The Names of G-d
G-d is not "the nameless G-d", He has many names.
The most important is the four-letter Name represented by the Hebrew letters Yod-Heh-Vav-Heh (YHVH). It is often referred to as the the Unutterable Name. It's Hebrew root is Heh-Yod-Heh (to be), and reflects G-d's existence is eternal. In scripture, this Name is used when discussing God's relationship to humanity, and when emphasizing his qualities of loving kindness and mercy. It is frequently shortened to Yah (Yod-Heh), Yahu or Yeho (Yod-Heh-Vav), especially when used in combination with names or phrases, as in Yehoshua (Joshua, meaning "the Lord is my Salvation"), Eliyahu (Elijah, meaning "my God is the Lord"), and Halleluyah ("praise the Lord").
The first Name used for G-d in scripture is Elohim. This Name is used in scripture when emphasizing G-d's might, His creative power, and his attributes of justice and kingship. Variations include El, Eloha, Elohai (my God) and Elohaynu (our God).
God is also known as El Shaddai. This Name is usually translated as "God Almighty". According to the Midrash, it means, "The One who said enough or sufficient and comes from the fact that when God created the universe, it expanded until He said "DAI!". The name Shaddai is the one written on the mezuzah scroll.

Writing the Name of G-d
Jews do not casually write any Name of God. This does not come from the commandment not to take the L-rd's Name in vain, as many suppose. In Jewish thought, this commandment refers solely to taking an oath, prohibiting swearing by God's Name falsely or frivolously (the word translated "in vain" literally means "for falsehood").
There is no prohibition concerning writing the Name of God; what is prohibited is erasing or defacing the Name of G-d. However, many Jews avoid writing any Name of God casually because of the risk that the written Name might later be defaced, obliterated or destroyed accidentally or by someone not knowing better.
The commandment not to erase or deface the name of God comes from Deut. 12:3. There, the people are commanded that when they take the promised land, they should destroy all items related to the idolatrous religions, and should destroy the names of all local deities. Immediately afterwards, the Hebrews are commanded not to do the same to G-d.
Normally, Jew's avoid writing the Name by substituting letters or syllables, for example, writing "G-d".

Pronouncing the Name of G-d
Nothing in the Torah prohibits pronouncing the Name of God. Indeed, it is evident from scripture that G-d's Name was pronounced in normal worship and discussion. Many common Hebrew names contain "Yah" or "Yahu," part of God's four-letter Name. The Name was pronounced as part of daily services in the Temple.
The Mishnah confirms that there was no prohibition against pronouncing The Name in ancient times. In fact, the Mishnah recommends using G-d's Name as a routine greeting to a fellow Jew (Berakhot 9:5). However, by the time of the Talmud, it was the custom to use substitute Names for God. Some rabbis asserted that a person who pronounces YHVH according to its letters (instead of using a substitute) has no place in the World to Come, and should be put to death. Instead of pronouncing the four-letter Name YHVH, "Adonai," is usually substituted. Often "Ha-Shem" (lit. The Name) is used.
Although the rabbinical prohibition on pronunciation applies only to the four-letter Name, Jews customarily do not pronounce any of God's many Names except in prayer or study. The usual practice is to substitute letters or syllables, so that Adonai becomes Adoshem or Ha-Shem, Elohaynu and Elohim become Elokaynu and Elokim, etc.
With the Temple destroyed and the prohibition on pronouncing The Name outside of the Temple, pronunciation of the Name fell into disuse. Scholars passed down knowledge of the correct pronunciation of YHVH for many generations, but eventually the correct pronunciation was lost, and we no longer know it with any certainty. We do not know what vowels were used, or even whether the Vav in the Name was a vowel or a consonant. Some religious scholars suggest that the Name was pronounced "Yahweh," but others do not agree.
Some people render the four-letter Name as "Jehovah," but this pronunciation is incorrect. The word "Jehovah" comes from the fact that ancient Jewish texts used to put the vowels of the Name "Adonai" (the usual substitute for YHVH) under the consonants of YHVH to remind people not to pronounce YHVH as written. A sixteenth century German scribe, while transliterating the Bible into Latin for the Pope, wrote the Name out as it appeared in his texts, with the consonants of YHVH and the vowels of Adonai, and came up with the word JeHoVaH. This incorrect name has been widely circulated in Christian churches, to the point it is widely regarded by most to be the name of G-d...

Webster's New World Dictionary: College Edition states (on pages 766-767 and pg. 1657):
1Je·ho·vah (ji hō'v[uh]) n. [[modern transliteration of the Tetragrammaton YHWH; the vowels appear through arbitrary transference of the vowel points of Adōnāi, my Lord: see Yahweh]] God; (the) Lord
2Yah·weh or Yahwe (yä’we, -wā) n. [[Heb, hypothetical reconstruction of the Tetragrammaton YHWH: first component, ya, Yahu, god < older Canaanite name]] God: a form of the Hebrew name in the old testament: ... : also Yah've or Yah·veh (yä've, -vā)