The short answer is it's impossible to do that currently.
Regarding group names, you cannot have groups with the same name. That is, you can't name the group "lights" for every room you want to control. If a group is named "lights" additional groups must be named something different.
As dragon123 stated, the alternative is to give each group a unique name such as "kitchen", "bathroom", "bedroom". If you have multiple bedrooms that you want to control, you must give each one a different name, e.g. "bedroom one", "bedroom two", "bedroom three", "John's bedroom", "Mary's bedroom". As you walk into a room, you would say "Turn on kitchen" or "Turn on bedroom two".
If you only have one light in each room, you won't have to create groups. Just name each one appropriately. Although you can create a group of one smart device, it is redundant. Groups should be used for something that's actually a group of 2 or more smart devices.
The ONLY way I can think of to accomplish what you want is to register every Echo device on a different account. Then each Echo can only control Wemo switches that you added to it. But that comes with a problem because if the Echo in the adjacent room hears you say "turn off the lights" it will turn off a different light. In my opinion, you'll lose far more than the convenience you gain. Prime music, calendar, to do list, drop-in/calls, Amazon delivery tracking, voice training, etc. will all be separate and a nightmare to manage.