Does your logo have a glyph?
We often use the “button” on its own, as do many other companies. We often refer to these “icons” as “glyphs.” Here’s another logo:
This company often uses the “o” as a stand-alone brandable element (the “glyph”). Some companies — like Starbucks and Apple — have even dropped the words from their logo altogether. Their logos are simply the glyphs and nothing else:
You’ll notice that in Starbucks’ case, the glyph is somewhat intricate in its artwork. This isn’t ideal, but it suits the company’s needs. Most of the time, designers will aim to make this shape simple so that it works well at all sizes and is easy to recognize.
In short, when choosing a logo for your company, go with something that is simple and contains a stand-alone icon that can convey your brand independently when necessary.