You're missing the driver. It's not like Google cares or wants to change the name. They more or less have to given the public/private relationship and who is responsible for what. It's not Google's job to name bodies of water, it's not a credit card company's job to censor. And if you actually look, they aren't making that decision because they want to. They are often acting on behalf of the government.
Payment companies are even more enmeshed with the state. They often do these things to simply comply with what the government tells them to do or to get ahead of government telling them what to do. Like with some of the anti-pornography laws being drafted or passed in certain American states.
The private/public distinction really needs to come under more scrutiny here. The credit card duopoly is very much tied in with state power. This has only accelerated post 9/11 as the Treasury's mandate increasingly shifted to "national security".
Payment processors are censors because the government is. Just like Flock the government can't do certain things so it contracts with a third party. They then have an interest in protecting/promoting that party. Flock is a snoop because the police are snoops. If Flock does it and the government merely pays for it well it's not a violation of your rights. Your rights protect you against the government, not against Flock. It's the same legal backdoor. A payment processor doesn't care what you buy, why would they? They make money so long as you keep transacting. It's the government that cares.
This same dynamic happens all over the American economy because the private/public distinction can get increasingly amorphous. Your credit card is as much government spyware as your phone. But understand - the problem is not the companies, it's the majority of your fellow citizens who either don't care or actually do endorse censorship. Unless you have a solution for that trying to blame credit card companies for the problem unfortunately misses the mark. You might as well suggest Google have the authority to name bodies of water.