The traditions which give a name to the daughter of Pharaoh are merely conjectural. Egyptian princesses held a very high and almost independent position under the ancient and middle empire, with a separate household and numerous officials. This was especially the case with the daughters of the first sovereigns of the 18th Dynasty.
Many facts concur in indicating that the residence of the daughter of Pharaoh and of the family of Moses, was at Zoan, Tanis, now San, the ancient Avaris (Exodus 1:8 note), on the Tanitic branch of the river, near the sea, where crocodiles are never found, and which was probably the western boundary of the district occupied by the Israelites. The field of Zoan was always associated by the Hebrews with the marvels which preceded the Exodus. See Psalms 78:43.
To wash - It is not customary at present for women of rank to bathe in the river, but it was a common practice in ancient Egypt. The habits of the princess, as well as her character, must have been well known to the mother of Moses, and probably decided her choice of the place.