The Collaborative International Dictionary of English v.0.48:

Logogriph \Log"o*griph\, n. [Gr. lo`gos word + gri^fos a fishing
   net, a dark saying, a riddle: F. logogriphe.]
   A sort of riddle in which it is required to discover a chosen
   word from various combinations of its letters, or of some of
   its letters, which form other words; -- thus, to discover the
   chosen word chatter form cat, hat, rat, hate, rate, etc. --B.
   Jonson.
   [1913 Webster]