The Muslim god Allah could be any god.

[CherubRam]

As an interpretation, "Allah" meaning, (The god,) could be any god.

Yahwah does not equal Allah.
Yahwah is a name and it means, "Life Began."
The word "God" is not a name, it is a title. Eloah is not a name, it is a title.
Holy Spirit is not a name, it is a title.

(Alla / Allah / Alilah) is a name, it means "the god ascends." Referring to the rising of the morning Sun.
The name Yahwah is written in the Hebrew text about 7000 times. About 50 times as Yah.
Yah is Life.
Most of the time the interpretation (The Lord) is given in place of God's name Yahwah.

(The God) does not define what god you are worshiping. It could be any god, so therefore Muslims do not know who they worship.

 

[Ted T]

The God) does not define what god you are worshiping. It could be any god, so therefore Muslims do not know who they worship.

...yet you name this god contradicting yourself...?

(Alla / Allah / Alilah) is a name, it means "the god ascends."

 

[CherubRam]

...yet you name this god contradicting yourself...?

Muslims say that Allah means "The god." The word is a name of a Pagan god.

 

[Mattathias]

The God I worship is the God of Israel / the God of the Jews.

I may have missed it but I don’t recall hearing Muslims say that they worship the God of Israel / the God of the Jews.