The Renunciant Life
Sannyāsa (from sam-ni-āsa = completely laying down) is the formal renunciation of all worldly identity, possessions, family ties, and social roles. The sannyāsi has no home, lives on alms, wears ochre robes (kāṣāya), carries a staff (daṇḍa), and is known by a spiritual name ending in -ānanda or similar.
Rāmānuja as Sannyāsi
Rāmānuja took sannyāsa in the Sri Vaishnava tradition (ekadaṇḍa — single staff, as opposed to Śaiva tridaṇḍa sannyāsa). He was formally ordained as a sannyāsi by his ācārya and took the name Rāmānujācārya. The Sri Vaishnava sannyāsi is called a yati.
Rāmānuja's unique contribution was his particular brand of sannyāsa that was not world-negating but world-serving — he used his sannyāsa not to retreat but to organize temple worship, reform the Śrīraṅgam administration, travel to Tirumala, and systematize the sampradāya. His sannyāsa was kainkarya in its purest institutional form.
Sannyāsa and Prapatti
The relationship between formal sannyāsa and prapatti is theologically interesting: one could argue that prapatti IS the ultimate sannyāsa — the complete renunciation of all other refuges and the surrender of the self to the Lord. In this sense, every true prapanna is a sannyāsi in spirit, even if a householder in form.