When initially seeking to name this project Ken ran into a problem every programmer encounters. What is a good name? It has to be descriptive, unique, and not too verbose. Additionally having multiple meanings would be a nice touch. Quickly ruled out were php*Something* names which, incidentally, although popular, do not seem to be condoned by the PHP Group developers. Drawing inspiration from Open Source projects like Apache, Mozilla, Gnome, and so forth resulted in two eventual choices: Dragonfly and Mantis. Dragonfly was already the name of a webmail package. So the name became Mantis.
Praying Mantis are insects that feed primarily on other insects and bugs. They are extremely desirable in agriculture as they devour insects that feed on crops. They are also extremely elegant looking creatures. So, we have a name that is fairly distinctive and descriptive in multiple ways. The BT suffix stands for "Bug Tracker" and distinguishes this project from general usage of the word Mantis. However, over time the project was typically referred to as Mantis.