I have not found the name "Al-Mawjud" (One that is given existence) among Allah's Names and Attributes, but I have found the Name "Al-Wajid" (One that gives existence to others).
I know linguistically, in Arabic, that a Mawjud requires a Mujid (another derivative that also means a being that gives existence), as there has to be a being that performs every action. However it is impossible that Allah has a Mujid. I also noticed that Al-Wajid has the same meaning as Al-Khaliq (the Creator) and that Al-Mawjud has the same meaning as Al-Makhluq (the creature). As there is a Mujid for every Mawjud and there is a Khaliq for every Makhluq, am I therefore permitted to describe Allah with the Attribute of Al-Mawjud?
The Wujud (existence) of Allah is a well-established religious matter by necessity, and it is one of Allah's Attributes according to the Muslim Ijma` (consensus). In fact, no rational person denies this; even the Mushriks (those who associate others with Allah in worship) do not dispute this. Only a Dahri atheist (one who believes all matter is eternal and denies the Day of Resurrection) would deny it. Confirmation of the Wujud of Allah does not necessitate Him having a Mujid, because there are two kinds of Wujud:
Al-Wujud al-Dhati, which refers to inherent existence, rather than an acquired one from elsewhere. This type of Wujud applies to Allah (Glorified be He) and it is one of His Attributes, as His Wujud had nothing before or after it, as is indicated in the following Ayah (Qur'anic verse):
He is the First (nothing is before Him) and the Last (nothing is after Him), the Most High (nothing is above Him) and the Most Near (nothing is nearer than Him). And He is the All-Knower of every thing.
(Part No. 3; Page No. 191)
Al-Wujud al-Hadith, which means that a being comes into existence after being nonexistent. In this case, there must be a Mujid to bring it into existence, and that is its Creator, Who is Allah (Glorified be He). Allah (Exalted be He) says:
Allâh is the Creator of all things, and He is the Wakîl (Trustee, Disposer of affairs, Guardian) over all things.
To Him belong the keys of the heavens and the earth.
Allah (Exalted be He) also says:
Were they created by nothing? Or were they themselves the creators?
Or did they create the heavens and the earth?
Accordingly, Allah (Exalted be He) may be described as Mawjud and this term may be used in reference to Him. It may be said that Allah is Mawjud as an Attribute, but it cannot be said that He is Al-Wajud (the Existent) as a Name.May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.