Senetnay was the wife of Sennefer, a vizier during the reign of Amunhotep II. They have a beautiful tomb in the Valley of Nobles. (There is some confusion about it, for Senetnay's name isn't mentioned in the tomb, and Sennefer's wife is called Meryt there, but maybe the two women are the same and Meryt, 'Beloved' could have been Senetnay's pet name.) They had two daughters: Mutnefert and Mut-Tuya.
About Tawy I don't know much; her name is probably a short form for Nebettawy (Lady of the Two Lands) or Henuttawy (Mistress of the Two Lands).
I know it's hard to pick up a name for yourself, I've been thinking for weeks before I chose mine! There are so many beautiful names in Acient Egyptian language. By choosing a name you can also show who is your favorite pharaoh, which is your favorite period in Egyptian history, that's why I have an Amarna name.
Also look around at http://www20.brinkster.com/neferuaten/names/fnames.htm
where I've collected a bunch of Egyptian names with their meanings, biography of those who had this name & the hieroglyphic form of the name. I hope it helps.