There is an interesting story as to how Raghavendra Theertha came to be known as Sri Raghavendra Swamy.
According to the records and notes on the life and times of Sri Raghavendra Theertha, the sage, during one of this regular tours, happened to stay at Bidarahalli, a village on the banks of the Tungabhadra River in Koppal District of Karnataka. There be had a chance meeting with a Sanskrit scholar called Srinivasachar, who was also a prolific writer having written many books on Dvaita philosophy.
During his stay at Bidarahalli, Sri Raghavendra Theertha noticed that the special mashi (ink) used for writing got exhausted. He asked his attendants to look out for the same kind of special ink used by him. They found the same kind of ink was used by Srinivasachar and bought it to Sri Raghavendra Theertha. After inspecting the quality of the ink and testing it, the sage summoned Srinivasachar. The Sanskrit scholar who came rushing to meet the sage also brought some of his works to be presented to him.
Sri Raghavendra Theertha, after going through the works of Srinivasachar, was surprised by the quality of his writing, in depth knowledge of Dvaita philosophy and rich grammar in his works. So, he gave the title ‘Theertha’ to Srinivasachar. From then on, he came to be known as Srinivasa Theertha.
Usually, the title is given to only those who give up worldly pleasures and accept sanyasa. In the case of Srinivasa Theertha, the sage as a special case conferred the title on the scholar. From that day, Sri Raghavendra Theertha himself came to be known as Sri Raghavendra Swamy popularly.
Source – Magazine Titled - Sri Raghavendra Swamy - The Living Saint of Mantralayam – published by The Hindu page 32