Yah is a proper noun, such as David or Deborah. The word "God" is a common noun.  When I was a teenager, the rabbi at my conservative synagogue wrote "G-d" on the blackboard and erased it.  Then he wrote "God" on the blackboard and erased it.  We were all shocked, considering most of us had been taught by parents and teachers that Judaism prohibited the the erasing or defacing of the word God or G-d.  When I wrote something for religious school homework and needed to discard a piece of  paper on which I made a mistake, if it had the word G-d on it, I was in a perturbing situation. Would I need to hold on to that paper for the rest of life or throw it away and await G-d's wrath?  The rabbi explained to us that those words were not the name of G-d, but merely common nouns.

We see in the Tanahk the Father G-d's name as Y'ah (yud hey) or Yahovah (Yud Hey Vuv Hey).  We have the y,h,v,and h consonants in his name but vowels were not in the written bible text.  Since we have no actual vowel sounds, we have no exact true pronunciation.  Yah is a shortened version of Yahovah.  When we say Halleluyah.  We are saying, "we praise Yah." 

Some say that his name is Jehovah.  This is from a lack of knowledge of the very basics of both the Hebrew and Latin languages. There is no "J" sound in Hebrew.  The origin of this serious error was a lack of understanding in using Latin orthography.  In Latin orthography "J" is pronounced as the English "Y."

We see in these verses from the Jewish Holy Scriptures, that our people in Biblical times did not hesitate to call Yah by his name.  Post Biblical Jewish tradition created a fence around the name, saying that it could only be used by the High Priest.  An interesting concept, but a man-made one.