Muad'Dib is the fictional name of two entities within the realm of Frank Herbert's Dune.

The first definition, found in the Terminology of the Imperium section of the Appendixes of Dune, defines muad'dib thus:

The adapted kangaroo mouse of Arrakis, a creature associated in the Fremen earth-spirit mythology with a design visible on the planet's second moon. This creature is admired by Fremen for its ability to survive in the open desert.

The second definition is broader in complexity.

It is the chosen name of manhood that Paul Atreides selects when he is accepted into the Fremen. It is one of two names that Paul maintains within the tribe. Stilgar explains that the first, Usul, means "base of the pillar". That it is his secret name, his troop name, that only Sietch Tabr may use and none other may presume.

The second, Muad'Dib, is that by which he is known openly. Stilgar explains that the choice pleases them and then goes on to explain:

Muad'Dib is wise in the ways of the desert. Muad'Dib creates his own water. Muad'Dib hides from the sun and travels in the cool night. Muad'Dib is fruitful and multiplies over the land. Muad'Dib we call 'instructor-of-boys.' That is a powerful base on which to build your life, Paul-Muad'Dib.

Paul is reluctant to throw away his full past and get rid of the full name his father gave him, which is why he is known as Paul-Muad'Dib. It would also seem that it has something possibly to do with his desire to escape his fate, however unsucessful he is at it.

The meanings of both Usul and Muad'Dib have powerful ramifications and loads of foreshadowing, for the purpose Paul is on Arrakis.