Do you use Serif or Sans Serif fonts for your brand?
When Cloud Media Marketing, LLC (CMM) was started, I created the logo of the purple cloud. When I started Feedable, a service of CMM, I wanted it to have the same tone, but I wanted it to stand out as a separate service. Using the blue for the words was a nice looking choice.
Having two colors in my logo has also made it easy for me to work the branding into content. I typically make headings purple and subheadings or details blue. Both colors look good on white or off white colors.
Did you know about serif vs sans serif? Serif fonts have "decorations" on the letters. These decorations make the words easier to read...in print. Sans Serif fonts do not have these "decorations" but are easier to read...on a screen. Most modern brands tend to pick sans serif fonts for this reason.