The Cardiff Railway Company no longer exists, and hasn't for many years.
In 2003 Arriva Trains Wales, the latest extension of the great Arriva network, took over the services previously operated by Wales and Borders, who were again previously known as Wales and West.
Arriva seem intent on retaining the name of the local train service in and around Cardiff itself - the white, green and red (the colours of the Welsh flag) Valley Lines trains which follow all the routes the Cardiff Railway Company used to - Cardiff to Barry and up the valleys via Cardiff Queen Street to Merthyr Tydfil, Rhymney and Aberdare via Pontypridd.
Sources: personal experience and http://members.aol.com/Walesrails/crc.htm