Why was the name "Ahmad" mentioned in the Holy Quran instead of "Muhammad" when referring to the Prophet, and is the name "Ahmad" correct for the Prophet, may Allah bless him and grant him peace?

The most famous of the Prophet's names, peace and blessings be upon him, are five, mentioned in one hadith: "I am Muhammad, and Ahmad, and I am Al-Mahi (the obliterator) through whom Allah obliterates disbelief, and I am Al-Hashir (the gatherer) after whom people will be gathered, and I am Al-Aqib (the successor)." These names were specifically mentioned because they are more renowned than others and are found in ancient scriptures and among previous nations. The name "Ahmad" also appears in the Quran.