When the Vedas were stolen from Brahma, Lord Mahavishnu took the Matsya avatara to retrieve them. We find in the Vishnu Sahasranama many names of the Lord that signify this avatara, said M.A. Venkatakrishnan in a discourse.
One of the names is Gururgurutamah. Guru and gurutamah are not to be taken as two names, but as one. It means that He is the highest among all preceptors, because He imparted jnana to Brahma. During the deluge, He steers the ship (earth), which holds the seeds of all that is dissolved during the floods. Hence, He is dhAmah. He is satyah, because He helped good people like Manu and others who sought His help. He is satyaparAkramah — His actions towards Manu and other virtuous people were in keeping with His prowess. He is nimishah, for He does not look with benevolence upon the enemies of His devotees. He is animishah, that is in the case of His devotees, He never closes His eyes. The name animishah fits the Matsya avatara perfectly, because fishes never blink. He is sragvee, the One adorned with a garland. Even when He takes the form of a fish, He is adorned with the Vyajayanthi garland. In the Matsya avatara, He gave to Brahma, Vedic knowledge that he had lost. Hence, He is vAchaspatih — the Lord of speech. He is udAradhI, because His jnana fills people with awe. He is agraNI, because He leads people to moksha. He is grAmaNI, because in Paramapada, He leads the Nityasuris. Lotus eyes are a feature of the Supreme One, and even in the Matsya avatara He has lotus eyes, thereby showing His Supremacy. Hence, He has the name SreemAn.
Desika, in Dasavatara stotra, says that the Lord’s movement in the ocean created the rise and fall of the waves resembling the movement of a swing, which the Lord enjoyed.