It is YEHOVAH not Yahweh
In Hebrew, the vowels used in Yahweh and YAH are different.
Yehovah and HalleluYAH are consistent with Yah.
We use the shortened version "Yah" for praise, prayer, and worship. It is the name used by David in the Psalms. Some NKJV translations print the name Yah where applicable. Psalm 68:4 is a prime example,
"Sing to God, sing praises to His name;
Extol Him who rides on the clouds,
By His name YAH,
And rejoice before Him."
Psalm 68:4 (Nelson, 2013)