Before you change name, you should receive any unclaimed premium item from Leonardo, and receive all items from Market Manager cabinet. When IAHGames offered the same name change service, there were some issues/bugs with faction/group/squad/friend lists:
However, once you change the family name, your friend list/faction list/etc will not be sync. Others may not be able to PM you but it will be resolved once maintenance is done. [Source]
Since the change is applied on weekly maintenance, this may not affect T3Fun players. If you do not want to take the risk, just leave faction/squad/group before the change.
There are also some concerns that scammers can reset their reputations by changing names... but I see too much problem with this, since each family can only change name once. If the family ever scams again, they will be known once more.