No, Allah has one identity and the attributes are just that: attributes. The names only describe His different attributes. It's like saying man has mind, imagination, power, life, dreams and wishes but he still has one identity.
To delve deeper, in Sufism, all attributes are non-existent compared to the Divine essence but rather they exist by the Divine essence existing. Think of the following statement:
The verb 'exist' according to Sufi theology represents the Divine essence, while the subject, 'life' is a property of existence/Divine essence. So things exist by the Divine essence existing. Or rather, they exist by Divine essence because existence and the Divine essence are one and the same thing. This is why they refer to Allah with the word حق which means 'real' and also why they refer to it with the word وجود meaning 'existence' or 'being.' Grasping this is really important. You'll learn that the attribute احدیه is a consequence of Allah construed as pure act of existing. That is, it is secondary to Allah being الحق, the real.
So ان الله هو الحق comes first, meaning "only Allah is real." Only = احد So by being real Allah is also only and alone because only He and He alone is real.
But then, how come other perceived things happen to existence if Allah alone is real? That's by Allah thinking Itself!
To see what it all means, comparisons to human soul is very useful as self-knowledge is the path to theology as a Prophetic hadith says.
So contemplate this: your thoughts exist only by the virtue of you existing. But they come only when you think them and when you don't they disappear but your being is still there and you're being is unitary احد and not multiple. But if you contemplate, even if you want to notice your own being, you have to think yourself, you have to be conscious. But if you transcend your mind and consciousness, you reach a state of as-if nothingness. You no longer even feel yourself or anything as if nothing exists. But this state is usually temporary in humans but it gives you a grasp of what the Divine essence or state of pure existence means which is ironically a state of as-if-nothingness. So existence and non-existence are one and the same thing epistemic-wise, in that it's a state that transcends every property or every 'thing' because it is a state that has no property, no feeling, no nothing by which you can describe it! As Sufis say and as @owari mentioned in his comment, the Divine essence ... لا اسم له و لا رسم له و لا ند له و لا ضد له و لا برهان له و. -- has no name and no sign or definition and no counterpart, and no opposite, and no evidence, and, I casually add, no nothing!
But once you let your thoughts and feelings emerge back, your attributes reveal themselves again, your mood, attitude, feeling, will, power, consciousness and so forth, they all come back. Therefore, as you see your attributes are secondary to your existence and wholly dependent on it and they also vaporize when you concentrate on your being alone, or your حق الأحدی; and gush out from your being when you allow your consciousness to come back. This is how everything emerges from as-if-nothing by self-consciousness.
Think of the Divine essence and attributes and essences in this vein. They all depend on the Divine essence and at the same time are nothing except the Divine essence, and all go back and disappear in the Divine essence.
کل من علیها فان و یبقی وجه ربک ذو الجلال و الأکرام
This was the essence of Wahdat al-Wujud, unity of existence in Sufi theology.