Depending on the company and the resources at their disposal, giving out running shoes or other equipment (or making them available at a discount) to employees at the start may be a better option. Chances are the employee who is the most active already has their own stuff. Though if it's a decent item, or one that people end up replacing a lot (like shoes, I suppose) it would work fine.
I really dig this idea, and I'll try to get it started where I work now.
"Fit Friday" definitely sounds the best out of the name ideas I've seen. Simple, and gets the point across.
Expanding on Lorena's idea, you could use pedometers, or some other workout-logging tool to create a competition within the company for who can achieve the most, either individually within a department, or collectively between departments (Sales vs. Support?). Fitocracy might be a decent tool for this, as it already gamifies working out.