The different titles of Ramanuja as per my knowledge are:
1. Ilayazhwar - ‘Young Azhwar’
This title was conferred upon Ramanuja by Thirumalai Nambi, at the time to Ramanuja’s birth.
2. Ramanuja - ‘Younger brother of Rama’
This name was given to Swami by Periya Nambi during Ramanuja’s Samasrayanam at Madhurantakam. It also signifies that Swami is the incarnation of Lakshmana (Adisesha), the younger brother of Rama.
3. Emberumanar - ‘My own master’
When Ramanuja revealed the Thirumantram to everyone at Thirugoshtiyur defying he orders of Thirugoshtiyur Nambi, the latter questioned the former as to why he did so despite knowing that he would go to hell. At that time, Ramanuja says that if for a hundred people to attain Paramapadam, he would willingly go to hell, replying to which Thirugoshtiyur Nambi lovingly called Ramanuja ‘Emberumanar’ meaning my own master.
4. Lakshmana Muni - ‘Saint Lakshmana’
This name was given to Ramanuja by Thirumalai Aandaan signifying that Ramanuja is indeed the re-incarnation of Lakshmana.
5. Godagraja - ‘Elder brother of Andal’
When Ramanuja fulfilled Andal’s promise to offer 100 pots of butter and Akkaraivadisal (sweet porridge) to Thirumaliruncholai Kallazhagar in Nachiyar Thirumozhi, he was lovingly called ‘Godagraja’, as he fulfilled Andal’s promise as a responsible elder brother.
6. Namkovil Annanar- ‘Elder Brother’
Andal herself also gave him the title ‘Anna’ meaning elder brother for the same reason as the above title of Swami Ramanuja.
7. Thiruppavai Jeeyar - ‘Acharya of the Thiruppavai’
On seeing Atthuzhai, the daughter of Periya Nambi at Srirangam, when listening to the Thiruppavai, he fainted from extreme emotion as he mistook Atthuzhai to be Nappinai; so absorbed was he, in the meanings of the Thiruppavai. Hence, he was given this name.
8. Yatirajar - ‘King of the Sannyasis’
This name meaning ‘King of the Yatis (Sannyasis)’ was given to Swami Ramanuja by Devadiraja Perumal / Varadaraja Perumal of Kanchipuram when Ramanuja accepted Sannyasa.
9. Desikendrar - ‘Indra of the Acharyas’
This title was given to Swami by Thiruvenkatudaiyan at Thirumalai.
10. Panchacharya Seedar - ‘Disciple of Five Acharyas’
Ramanuja had five Acharyas:
Thus, he was given this name.
11. Appanukku Sangaazhi Alittha Perumal
Ramanuja resolves the dispute of whether the deity at Thirumalai is Vishnu or Shiva. Thus, he was given this title.