Al-Zamzami is one of the names of our Master, the Prophet (Allah bless Him and give Him peace).
The authors of works of prophetic biography (sirah) mention a number of names for Him (Allah bless Him and give Him peace) which are based around the word Zamzam.
Imam al-Salihi in his lengthy chapter on the prophetic names in his ‘Subul al-Huda wal-Rashad’ (1/468) mentions approximately five hundred (500) names, amongst them being ‘al-Zamzami’. He referenced this name to Ibn Dihyah. The other names which he mentions are:
‘Sahib al-Zamzam’ which he also referenced to Ibn Dihyah.
‘al-Muzamzam’ referenced to Allamah al-Zayni Abd al-Basit Ibn al-Imam Muhammad Badr al-Din al-Bulqini,and that He (Allah bless Him and give Him peace) was named ‘al-Muzamzam’ when His blessed heart was washed with zamzam water.
‘Nabi al-Zamzam’ The Prophet (Allah bless Him and give Him peace) took control of the well of Zamzam in the year of the Makkan conquest.
Scholars named ‘al-Zamzami’
From the scholars that were given this prophetic name are:
Sh. Muhammad al-Zamzami ibn al-Sayyid Muhammad Jafar al-Kattani who passed away in the year 1371 (AH)
Some scholars, it is mentioned, were given this name due to their association with the actual well of Zamzam itself, amongst them being:
Imam Ibrahim bin Ali bin Muhammad al-Shambari al-Makki al-Shafi al-Zamzami, who passed away in the year 864 (AH)
Allamah Abd al-Aziz bin Ali bin Abd al-Aziz al-Zamzami al-Makki al-Shafi, he was a scholar of hadith, jurist and poet. He authored a collection of rulings called ‘Fatawa al-Zamzamiyah’. He passed away in the year 963 (AH)
Allamah Khalifah bin Abi al-Faraj al-Zamzami, author of ‘Nashr al-Aas fi Fadail Zamzam wa Siqayah al-Abbas’
Imam Abd al-Aziz bin Muhammad bin Abd al-Aziz al-Zamzami al-Makki, the Shafi jurist. He was born in the year 977 (AH) and passed away in Makkah in 1072 (AH)
Other scholars have been mentioned in the works which have been cited from above
 Al-Sakhawi has a biographical entry for him in his al-Daw al-Lami’ (3/28). He mentions in it that he arranged the prophetic names into a poem which he authored.
 Refer to his biography in Mujam al-Muallifin (13/418).
 He has a biographical entry in: al-Kawakib al-Sairah (2/170) and Mujam al-Muallifin (5/254).
 Refer to Nazm al-Durar (p.73) for the biography of Allamah Ibrahim bin Muhammad bin Abd al-Latif al-Rais al-Zamzami al-Makki, who passed away in the year 1195.
Also refer to (p.146) which contains the biography of Sh. Muhammad bin Ali al-Zamzami al-Makki, one of the notable Makkan scholars from the 13th Islamic century. The date of his passing away is not mentioned.