civilization-6civilization-6-rise-and-fall
I haven't noticed a penalty for capturing Free Cities so far in Rise and Fall.
Even when an opposing Civ had it's final city declare independance and then I captured that city, I didn't experience the expected drop in diplomatic relations for wiping out a Civ.
Has anyone found evidence that this is indeed the case? I couldn't see anything about it in the Civilopedia.
City Renaming has been added with the Fall 2016 update:
Open the city details pane (the highlighted page icon on the panel) and click on the city name in the top left corner of the screen
I haven't confirmed this, but I believe that you can only bring up this topic of discussion after one of your cities has been converted.
Note that using a missionary does not mean your city is converted. Conversion happens when the majority of citizens follow a religion. If a single missionary was used it may be that only some citizens became swayed, but not the majority.
I have found that the AI never brings this up with me until I fully convert at least 1 city.
Best Answer
I've tested this a few more times, and from what I can see there is no Warmonger penalty for caputuring a Free City, even if that Free City used to be the last remaining city of an enemy Civilization.
As has been mentioned, this is likely to prevent you suffering a warmonger penalty for taking your own rebellious cities back by force, but it does provide an amusing (if situational) way to wipe out an AI civ without suffering the "captured a Civ's last city" warmonger bonus.