In 6.0 hstgrp table had index by name. In 6.2 it was changed to unique index by type and name. When syncing configuration with proxy only groupid is sent. When discovery group is changed it causes SQL error because proxy is trying to insert another group with the same (default) name and type.
The simplest fix would be to mark hstgrp name and type with ZBX_PROXY in schema template, so they also are sent to proxy.