If I change an AD security group name from "name1" to "name2". Will that effect foldershares that are shared out to the group "name1"? Will it automatically be updated to "name2", or will I get trouble?
That don't have any effect on folder shares. Groups are identified by SID which doesn't change if you change group name. If you go to that folder share and take a look at security tab, then you might see old group name there, but it doesn't matter.