Baha'u'llah converted to Babism at the age of 27, at the age of 31 he chose the name 'Baha' for himself.

In 1844 Mirza Husayn Ali received a visit from Mulla Husayn, one of the Bab’s early disciples. The Bab sent Mulla Husayn to Tehran to deliver a letter to Mirza Husayn Ali (Baha'u'llah), he converted to Babism at the age of 27.

In 1848 Mirza Husayn Ali organized and helped to direct the gathering of Babis in the village of Badasht; this conference at Badasht gave Babism a new and more revolutionary direction. It was also at the Badasht Conference that Mirza Husayn Ali gave each of the Babis gathered there a new name, one that reflected their spiritual qualities. For himself he chose the name Baha, which means “Splendor” or “Glory.”

(WORLD RELIGIONS - BAHA’I FAITH, THIRD EDITION by Paula Hartz, Page 41)