Dark Souls was more than a name change.
Demon's Souls was a hub world, whereas Dark Souls is open world
Demon's Souls used grass as the healing option whereas Dark Souls had the estus flask
Demon's Souls had the Nexus whereas Dark Souls had bonfires
Demon's Souls had world tendency events
There was plenty room for Demon's Souls and Dark Souls to coexist
They were similar enough though. Who's to say that From wouldn't have gone in that direction even without the branding change? We'll never really know.