In the canon story of the games, the Umbrella Corporation was shut down by the government in 2003. The only name it was known by was Umbrella, followed by the abbreviations Corp., Inc., or lesser known as Umbrella Pharmaceuticals.
The company that rose to prominence after Umbrella's shutdown was named Tricell. Tricell is an entirely different entity that Umbrella, though. It is not a new name for the Umbrella Corporation.