(DeCandido's novelizations of the Anderson films)
Verizon was a American telecoms company. It had a monopoly on landline telephones in Raccoon City. This became a problem for the Umbrella Corporation during the Raccoon City Incident, as they were unable to prevent people within the city from telephoning the outside. Dr. Ashford, upon realising this, was able to contact Alice Abernathy.
In the Anderson films it is instead Umbrella's own telecoms company, "Umbrella TeleSystems", which has a monopoly on the landline phone network in the city.