How did he get such a name you might wonder?
He was said to break into structures using stealth on feudal missions and he kept mice or rats in a bag which he would release if necessary as a distraction. If he made a noise that alerted guards, he would release the rat and run away or at least that's the legend. The rat would distract the guards and create confusion which he would use to get away. Some superstitious guards, probably unwilling to admit their own mistakes, claimed that the ninja had turned into a mouse, and so the legend goes.
We can learn a lot from animals like the rat, mouse or even raccoon. They are patient, quick, clever, agile, and very persistent. Of the various lineages taught in the Bujinkan (Soke Hatsumi's Ninjutsu Organization), Togakure Ryu is lineage that actually has techniques that fall into a grouping which translates as "run away like a mouse skills". These techniques consists of trying to get away from an attacker when one has been seized primarily.
Whereas many martial celebrate the fighting prowess of various of animals. It is not the fighting abilities that we look to in using the paradigm of a rat or mouse. It is the animal's ability to free itself from a dangerous situation and its ability to remain unnoticed and blend into its hiding places that we praise.