Until WW II, there was a second telegraph company in the United States, known as Postal Telegraph. (They had nothing to do with the post office, just took the name to sound cool). They were a smaller outfit, but in competition with Western Union. Here is an ad (two pages)
They ran into financial trouble and merged with Western Union.
WU's well respected president, Walter P. Marshall, was originally a PT employee.
As an aside, there was another telephone company, Keystone Telephone, that competed directly with the Bell System in a few places.
They too fell onto hard times and were merged into the Bell System.