[NorFoster]

The name BlackBerry was given to the RIM phones because the first phone made in this series had the keypad like the seeds of a fruit.
Many fruits were idealized for small seed size and at the end blackberry was chosen because the color of all the gadgets was black.

[tsac]

A little more info

The name BlackBerry was coined by the marketing company Lexicon Branding. The name was chosen due to the resemblance of the keyboard's buttons to that of the drupelets that compose the blackberry fruit.