Yeah, but it was just a rename, despite that, the entire lineage stands. When the WWWF became the WWF, the title name changed but the history remained. Its like whenever they've replaced the physical belts, they've still represented the history and prestige of the original title belt. (although the current WWE title belt is disgraceful!)
When Ric Flair jumped ship to the WWF from WCW, he took with him the NWA World Heavyweight Championship, which at that point was WCW's World Championship. This was the "Big Gold Belt" and because the champion was required in those days to put down a deposit (in case the belt was damaged whilst in their possession) Ric Flair and others would often leave the deposit to gather interest as they would be getting the title bank at some point. When Ric Flair fell out with the NWA and WCW, he took the belt with him since they refused to return his deposit (and he refused to lose the title clean on his way out). Therefore WCW created their own belt and broke away from the NWA. When Flair returned, because WCW owned the physical belt they added the WCW logos and branding to it and renamed it the WCW International Championship. In a unification storyline, the belt eventually became the physical represenation of the WCW World Championship once again.
Like most wrestling companies, WCW had two of every championship (one that was used on TV, PPVs and houseshows, the other that the champion took on the road with them). When Hulk Hogan was champion during the NWO storyline, they had another replica built so they could spraypaint NWO over it and not ruin the original belt. When WWE bought WCW out, they naturally acquired all the belts, they used the WCW World Championship up until the day after Wrestlemania 18, where Triple H was presented with the WWE Undisputed Championship belt. When the World Heavyweight Championship was being brought into play, WWE commisioned a new belt made to look almost exactly like the "Big Gold" belt but with the WWE logos and trademarks built into it and of course "World Heavyweight Champion" as opposed to "Heavyweight Champion Of The World" when it represented what were the NWA and WCW World Championships.
Wrestlers who win championships will often have replicas made for themselves. We've seen Team 3D for example appear with every tag team championship belt they've won during a storyline a while back in TNA. The Rock has replicas in a trophy cabinet at his home too. Rhino was allowed to keep the ECW Championship belt when the company folded (WWE would later make their own replica based on this design) and most of the retired title belts are kept at WWE HQ, brought out for exhibition at events like Fan Axxess.
