CC Ādi 5.124

eta mūrti-bheda kari’ kṛṣṇa-sevā kare
kṛṣṇera śeṣatā pāñā ‘śeṣa’ nāma dhare
Synonyms: 
eta — so many; mūrti-bheda — different forms; kari’ — taking; kṛṣṇa-sevā kare — serves Lord Kṛṣṇa; kṛṣṇera — of Lord Kṛṣṇa; śeṣatā — ultimate end; pāñā — having reached; śeṣa nāma dhare — assumes the name Śeṣa Nāga.
Translation: 
He is thus called Lord Śeṣa, for He has attained the ultimate end of servitude to Kṛṣṇa. He takes many forms for the service of Kṛṣṇa, and thus He serves the Lord.