Why are the following names considered names of Allah, even though they appear in the texts without the definite article, and are not considered merely attributes, such as Hayy, Sattir, and Muhsin?

The questioner : Regarding the names of Allah (Mighty and Majestic), such as Hayy, they do not have the definite article as they appear in the texts.

The Shaykh : Yes.

The questioner : And the question is, why are they considered names of Allah (Mighty and Majestic)?

The Shaykh : What did you remember?

The questioner : Why are they considered names?

The Shaykh : What are the names you mentioned?

The questioner : Hayy, Sattir, and Muhsin appear in the texts without the definite article.

The Shaykh : What is the connection of the definite article? When something is a proper name, is it necessary for it to be defined, in addition to being defined by being a proper name, that it also be defined by the definite article?

The questioner : I do not mean why do we not consider these attributes rather than names, Hayy and Sattir?

The Shaykh : When we ask why it is not the case that it is a name and an attribute, what prevents us from saying that it is a name and at the same time every name includes the meaning of an attribute of Allah (Mighty and Majestic)? What is the prevention from saying that this is a name and at the same time an attribute? The prevention that emerges from the way the question is phrased is that it is not defined, so the previous objection was raised. It is not a condition of a proper name that it be defined; Muhammad, Ahmad, and so on are proper names, and it is not necessary for them to be defined. This is what appears to me, and Allah knows best.
The student : Our Shaykh, we found responses.

The Shaykh : What Allah willed.
The student : Praise be to Allah.