Is it permissible to perform remembrance (dhikr) using the Most Beautiful Names of Allah, and should it be done by reciting the Names as they were revealed, such as: "He is Allah, the Most Gracious, the Most Merciful, the Sovereign, the Most Holy," without a specific number or alteration?

The prescribed way is to supplicate Allah using His Beautiful Names. Among the forms of deviation concerning them is inventing a method not practiced by the Prophet, peace and blessings be upon him, nor by his companions, such as repeating a single name like "Hayy, Hayy" (The Ever-Living) or "Allah, Allah." This falls under innovations. However, reciting Allah's Names as found in the Quran and Sunnah is permissible, as long as it constitutes a complete and meaningful statement, unlike the single name which is not prescribed in any book or Sunnah, nor is it authentically reported from the predecessors (Salaf) or the eminent figures of the Muslim nation.