The name "Al-Qur'an" is derived from the Arabic root qa-ra-a, which means "to read" or "to recite." Accordingly, Al-Qur'an literally means "The Recitation" or "That which is recited." This name reflects the fundamental nature of the Qur'an as a text meant to be recited aloud, memorised, and transmitted through oral recitation - a practice that began with the very first revelation when the angel Jibril (AS) commanded Prophet Muhammad (SAW) with the word Iqra' ("Recite!") in the Cave of Hira.
The Qur'an is the final holy book revealed by Allah, sent down over approximately 23 years. Its identity as "The Recitation" distinguishes it from other scriptures in that its preservation has always been tied to oral transmission alongside written recording. Millions of Muslims (huffaz) memorise the entire text, making it the most widely memorised book in history.
The other options are not accurate translations of "Al-Qur'an": "The Law" would more closely correspond to the Torah/Tawrat. "The Testament" is associated with Christian scripture terminology. "The Reminder" (Adh-Dhikr) is indeed one of the names used for the Qur'an in the Qur'an itself (Surah Al-Hijr, 15:9), but it is not the meaning of the word "Al-Qur'an."