The story
The Movistar brand has been in use in Spain since the launch of GSM services in 1995. The name became effective worldwide on April 5, 2005, after Telefónica purchased the BellSouth mobile operations branch in South America. After the purchase of O2 in 2005 by Telefónica, the company announced that the «O2» brand would continue to be used in the United Kingdom and Germany, as a separate branch with its own board and management structure. Since 2011, Telefónica has sponsored a UCI ProTeam squad in cycling under the name of Movistar Team.
Since 2019, Telefónica has decided to divest all of Movistar's operations in Latin America, with Venezuela being the only country in Latin America who has Movistar and being directly owned by Telefónica (Movistar México is owned by a third-party company who continues to use the Movistar name under a license agreement, and Brazil uses the Vivo brand instead of Movistar).
From Wikipedia’s article on Movistar, shared under CC BY-SA 4.0.4