Name of varuNa's wife is gaurI as per mahAbhArata anuShasana parva CLXV and udyoga parva CXVII :
then the illustrious Sakra the lord of Sachi; and Yama with his spouse Dhumorna; and Varuna with Gauri; Kuvera the lord of
treasures, with his spouse Riddhi;
And the royal sage then sported with her, as Surya with Prabhavati, Agni with Swaha, Vasava with Sachi, Chandra with Rohini, Yama with
Urmila, Varuna with Gauri, Kuvera with Riddhi, Narayana with
Lakshmi, Sagara with Jahnavi, Rudra with Rudrani,
vArunI is the daughter of varuNa and wife of sheSha as per harivamsa Chapter 41 :
sAsmi pUrNena yogena yaithavAmR^itamanthane | samIpaM preShitA pitrA varuNena tavAnagha ||2-41-21
O one without sins! I am that one, fully suitable (to you) who was sent by my father varuNa to
you during the days of churning for nectar (amR^ita).
balaM jayasya daityAnAM baladeva divIshvara | ahaM te dayitA kAntA vAruNI samupasthitA ||2-41-17
O the god of deva-s! baladeva
(balarAma)! Let there be victory to you. You are the strength of
deva-s against daitya-s. I, vAruNI, your dear wife, am standing
near you.