The 72 Names
In Judaism, the name of G'd is representing the divine nature and the relation between him and his people. To show the holiness of G'ds names the scribes paused before copying them and used reverences to keep his true name concealed. Various names of G'd in Judaism represent G'd as he is known and in the attributes that are kown from him.
The numerous names have been source to many debates amongst scholars. G'ds most important name in Judasim is the Tetragrammaton- four letter name(YHWH). It appears 6828 times in the Bible. In times when the Temple was still standing the High Priest pronounced him on Yom Kipur.
The jewish Law requires that secondary rules are placed around the primary law, to reduce the chance that the main law will be broken. As such, it is common Jewish practice to restrict the use of the word Adonai to prayer only. In conversation, many Jewish people will call G'd "Hashem".
Adoshem was commonly used until the mid twentieth century. It was discouraged by Rabbi David ha Levi Segal. He said it was disrespectful to combine a name of G'd with an other word.

Adonai
The singular is Adoni- my Lord"and was given instead of YHWH in the 8th century. Later it was mistakenly pronounced as Jehovah.
Ehyeh Asher Ehyeh
In this name G'ds Potency for the immediate Future is shown. It's interpretation is: "I will be because I will be". The four letter name might come from the same root.
El
The word El appears in other semitic languages. Often it is an element in proper names. The use is for singular and plural- for other G'ds and for the G'd of Israel. In hebrew names it is often the ending such as in f.e.Daniel, Michael. Sometimes it attributes G'd such as in El Shaddai ( G'd Almighty)
Elohim
In the Bible it is often used to also describe other G'ds of other religions. Even though it ends with an ending that is commonly used for plural, it has a meaning that is only singular. It expresses majesty and greatness

Elyon
This name occurs in combination with El, YHWH or Elohim. It's meaning is supreme.
Shaddai
Shaddai was a city on the banks of Euphrates river. In the Bible it comes from the Vision of Balaam coming from Shaddai along with El. According to the second Book of Moses it was the name that was known to the three forefathers. Some say it is connected to the hebrew word" Shadayim"- Breasts. "By the Almighty [El Shaddai] who will bless you with blessings of heaven above, blessings of the deep that lies beneath, blessings of the breasts (shadayim) and of the womb (rechem)"
Shalom - Peace
It is said in the Talmud that the name of G'd is Peace. Consequently it is said that one is not allowed to greet someone in a dirty place."
Shekhina
Shekhina is the Presence of G'd which is descended to the world. This term never appears in the Bible. It is the only term that refers to a feminine gender.
Yah
The name Yah is composed of the first letters of YHWH.

YHWH Tzevaot/ Sabaoth

It means G'd of Hoasts. The original meaning can be found in Samuel naming the" G'd of armies".
Ha Makom - the Place
Used in the traditional expression of condolence.

Ehiyeh sh'Ehiyeh, Elohei Avraham, Elohei Yitzchak ve Elohei Ya`aqov, El ha-Gibbor, Emet, E'in Sof, HaKadosh, Baruch Hu, Kadosh Israel, Melech HaMelachim, Makom or HaMakom, Magen Avraham, Ribbono shel `Olam, Ro'eh Yisra'el, YHWH-Yireh,YHWH-Niss"i, YHWH-Shalom, YHWH-Ra-ah, YHWH-Tsidkenu, YHWH-Shammah, Tzur Israel,

Seven names of G'd:
1. El
2. Elohim
3. Adonai
4. Ehyeh Asher Ehyeh
5. Four letter name
6. Shaddai
7. Zebaot

Lesser used names of G'd:
Adir - "Strong One".
Adon Olam - "Master of the World"
Avinu Malkeinu - "Our Father, our King".
Awinu Malkinu
Boreh - "the Creator".

Kabbalah:
One of the most significant names is the Ein Sof ( Infinite). The 42 lettered name is containing combined names.
The book Sefer Yetzirah explains that the creation of the world was achieved by the manipulation of the sacred letters.
According to Jewish tradition, the sacredness of the divine names must be recognized by the professional scribe who writes the Scriptures. Before writing any of the divine names he prepares mentally to sanctify them. Once he begins a name he does not stop until it is finished. He must not be interrupted while writing it, even to greet a king. If an error is made in writing it, it may not be erased, but a line must be drawn round it to show that it is canceled, and the whole page must be put in a genizah (burial place for scripture).

Tradition of 7 Names
The scribe must be especially carful with these names: El, Elohim, Adonai, YHWH, Ehyeh-Asher-Ehyeh, Shaddai.