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Where did you get this from? Could you provide a link?

I have to ask because this sounds bogus to me. I have never seen anything in the Qur'än or Sunnah to suggest that these names particularly refer to the different levels mentioned. The names Al-Jahïm, Jahannam, As-Sa`ïr, Saqar, Ladhä, Häwiyah and Al-Hutamah are NOT different levels of Hell, but rather, different names and attributes of Hellfire. Of course, there are different levels and different types of torment fitting the sin, but I've never seen this before.

I have read about this in more than one source before.

For example, it was called

جحيم
Jahïm: Named so due to the strength of its flames.

جَهَنَّم
Jahannam: Named so due to its extreme depth

السعير
As-Sa`ïr: Named so due to because it is fueled. [Example: أسعر النار As`ara Annär = He fueled the fire]

سَقر
Saqar: Named so because of its intense heat

لظى
Ladhä: Named so because it blazes

هاوية
Häwiyah: Named so because of the great long distance an object would travel while falling down through it. [Example: The word is used in every-day Arabic. It literally means: "Cliff" or any naturally forming high area where a person may have a dangerous fall. It is related to the verb هَوى Hawä = He fell, and its present tense يَهوي Yahwï = He falls]

الحُطمة
Al-Hutamah: Named so literally because it shatters and breaks whatever falls into it. [Example: This word is related to حَطَّمَ Hattama = He broke, or shattered (something)].

You're welcome!

BTW, I searched all the major compilations of hadith, and all original and modern books of tafsïr for the word "Ladhä". Only one book of tafsïr by Tantäwï mentioned that while it is most likely one of the names of Hellfire, some claim it is one of its levels.

First of all, there is no hadith, nor book of original or modern book of tafsïr claiming that "Ladhä" is the abode particularly of Christians, nor is there any significant mention of it being one of the levels of Hellfire (in contrast to it being one of its names).

Looking at the particularly Sunni books of tafsïr, most also agree that "Ladhä" is a name of Hellfire, and the very few who mention the possibility that it may be merely a level are skeptical about that explanation, let alone any association of it with Christians.

To put it simply, the only mention in the Qur'än is actually general, and does not at all name Christians particularly (See Sürat Al-Ma`ärij 70:15)