To know the origin of the name Columbia we have to travel back all the way to 1738 when it was published in the weekly publication of the debates of the British Parliament. It was forbidden to print the debates and to camouflage this they were published as Reports of the Debates of the Senate of Lilliput. Fictional names were thought up for other countries and Columbia was the one used for America, the one responsible for this is most probably Samuel Johnson. The name finally became the female personification of America and was chosen to be the name and logo of the company.
Sources and further information:
The Story Behind… The Columbia Pictures Logo