Apparently I was wrong. The way that I described it, it did not work at all.
But upon checking my settings, I saw that my Wemo light switches and Wemo smartplugs were all under the "switch" classification in the Alexa app. When I changed it from "switch' to "light" and then followed the directions from dragon123 above, it all worked. So now, I can walk into a room and say "turn on the light" and the appropriate light will turn on.
The group name, the Echo device name, and the smart device name really doesn't matter. You're going to put them in one group anyway. For multiple rooms, just repeat and use a different group name.
I am pretty sure that every type/brand of smart device will be a little different. But the main point here is to make sure it is configured as a "light" in the Alexa app. At least for Wemo, this is absolutely necessary.