The company wants workers who are forced to go through company switchboards for directory enquiries to use its website.
It is also looking to introduce 18 to 35-year-old mobile phone users to the site.
Incumbent agency Brazil PR, which promoted the firm's heavily advertised launch campaign following the end of 192 services, declined to repitch for the £150,000 account.
Ten agencies submitted credentials and Cow won the work in a four-way pitch.
It emerged earlier this week that The Number chief executive Chris Moss is to become European chairman of the company.