What is the word for a backless sofa?

A chaise longue / chaise lounge (american) has a very low or no back at all see www.distinctivechesterfields.co.uk/shop/browse_ranges/chaise_longue.html for details

Divan.........A long upholstered seat typically with a back and arms.

[Turkish, from Arabic uffa, carpet, divan, from Aramaic ipp, absolute form of ippt, mat; see pp in Semitic roots.]