The agency will produce a one-off campaign that will run predominantly in Spain, announcing that the Telefónica brand will now be known as Movistar.
It will also run in some Latin American markets where the Telefónica brand is established and will include TV, print, posters and in-store activity. Telefónica will become a shareholder-facing corporate brand.
The news follows Telefónica's appointment of Mother to the global advertising account for Movistar.
The appointment will see the agency devise a global strategy for the Movistar brand, as well as through-the-line campaigns set to run in all of Movistar's markets.
That activity will follow Publicis' initial campaign announcing the rebrand.
The appointments come as part of an overhaul of Telefónica's marketing arrangements. The telecoms giant, which spends around £250 million on advertising globally, recently kicked off a review of its £100 million pan-European O2 media account.