Pachirisu's English name has been officially declared to be Pachirisu, apparantly, much in the manner of Pikachu, Pichu, Raichu, Plusle, Minun, and any of the other electric rodent Pikaclones so far. >>
In case you wonder, Pachirisu derives from pachiri (meaning quickly, suddenly, 'lightning-fast' so to speak) and risu, meaning Squirrel.
Curiously enough, 'pachimon' in Japanese means a 'cheap imitation of a famous brand'. Which also makes sense, considering the fact that indeed, Pachirisu is a cheap imitation of Pikachu.