Eurybatus was the twin of Olus, with both brothers being the two Cercopes who harassed Heracles. His name means 'wide walker', from eurys, 'wide' and baino, 'to walk'. This is not so much a propitious name as a descriptive one, since he roamed abroad doing mischief.

By a happy coincidence, the sense of 'wide' here is almost exactly that of the English word in the slang 'wide boy', where 'wide' (according to the Concise Oxford Dictionary) means 'skilled in sharp practice'. That was Eurybatus exactly.