SharePoint should internally manage the change , as associations inside SharePoint are done using the uid and not the name.
Where you may have problems is if you have any third party code that looks up groups based on names, which is the default mechanism of indexing into a collection of groups.
Bottom line, if you don't have any third party code - you should be OK. If you do, then focus your testing on this.
var url = "http://mysp/";
using (var sc = new SPSite(url))
using (var s = sc.OpenWeb())
// following statement fails with 'Group cannot be found.' if Test is renamed
var group = s.SiteGroups["Test"];