Yes you can. When you rename the variable it should update all the cards that use it. Before or after changing it you can RMB on the variable and pick "Show where the variable is used". doing this you can double check to make sure it has been changes.
You will not mess up anything that won't be fixed if renaming the variable back to the original name again. Enterprise usually references variables by their internal ID, not by the name, so changing the name should not cause a problem. There are a few exceptions to this rule however:
1. You may have written your own API-extensions that reference the variable by name. They will of course stop working if the name is changed.
2. You may have used the variable in a template. Templates reference variables by name so you need to update the variable name by hand in the template too.
3. You may have set up export/import of XML data to interface with another system. The XML-file will reference variables by name unless you are using an "alias set".
4. You may have created a task script (in Enterprise 2010) that reference variables by name.
If any of these cases apply to your installation, you will have to make sure that the variable is renamed there too.
Hope this helps,