In the Hebrew Bible, God's name is YHWH. The ancient Hebrew alphabet didn't contain any vowels, and the vowel sounds used in words were passed down as part of oral tradition. Unfortunately (for us), the ancient Hebrews would not speak the name of God for fear of using it in vain, so we may never know exactly how it was pronounced. Historical linguistics, though, suggest that it was pronounced "Yahweh" (YAH-way).
If Father, Son, and Holy Ghost aren't names, what is God's name?
When people began translating the Old Testament into Western languages, some reasoned guesswork went into filling in the vowels, and the name of God was translated, ultimately, into Jehovah. (JHVH isn't a far cry from YHWH.) Some religious sects (particularly Jehovah's Witnesses) claim that this is the true name of God. However, historical research supports the idea that the original pronunciation was "Yahweh," especially considering that there was no "J" sound in ancient Hebrew.
The concept of the Trinity — Father, Son, and Holy Ghost — was introduced in the Church during the 4th century, after Constantine became emperor and persecution of the Christians by the Roman Empire was relaxed enough that elders could meet and make decisions about Church doctrine. The concept of the Trinity describes the three forms that the Church believes God has taken in his interactions with people here on Earth.
In Islam — which, like Judaism, claims to be descended from Abraham — God is called Allah. Actually, Muslims believe that Allah is just the greatest of God's name. The Koran teaches that there are 99 other names of God, each name evoking a distinct characteristic of God. Some of those 99 names are As-Salam ("The Source of Peace"), Al-Khaliq ("The Creator"), and Ar-Raqib ("The Watchful One").
Of course, many other religions have many other godly names — and many other gods as well.