I think it will certainly have to happen. The most recent letter form the Producer has short paragraph on server merges.

The server merge is a temporary measure intended to help FFXIV progress. We’ll be reintroducing Worlds when the number of players demands it, and with relaunch of version 2.0.
If worlds are being reintroduced which I take to mean people have to choose their world again, then there could be mayhem with the number of identical names. So I would imagine a name change will be forced by default for everyone.