Which isn’t really a problem you can solve. If names change in the context that they’re used, it will always be broken, so why break more names by trying to be clever?

I'm not saying you can solve it. A single text field isn't a solution either. You cannot avoid breaking some names.

A single field breaks fewer names than forced first and last names, though, and is a simpler implementation too. Plus, as long as you accept any input (besides blank, I guess), then the only way it will be broken is during display and at least the user sees the exact name they typed in, exactly how they typed it in.

A single field also breaks the expectation that people do not get called by their full names in every interaction. This is a very common expectation, and violating it makes you sound subtly more like an evil robot.

Is this a lesser offense than mangling a name that doesn't cleanly split into first/last? At the individual scale, probably.

The impact, in aggregate, on UX/sales/utility? Could definitely go either way depending on your userbase.

That's not an evil robot, it's a polite robot.

Better than the slimy feel I get when a robot calls me just by my first name. You're a robot, we're not buddies.

Actually I think it should be ok, because you’d enter the name in the nomative case and then when you write it on the screen you’d declinate it based on the language you’re displaying it in, which would be the same for every name regardless of its origin.

Tried that once. Horrible, terrible, no good idea. (The only rule you can be sure of is "there are countless exceptions, and exceptions from the exceptions", everything else is a minefield in a quicksand) Asking for "how should we address you" is far easier, even if a few users fill in "Your Galactic Imperial Majesty".

What’s this? A name that changes when you are talking to someone directly? In some Slavic languages this happens.

Usually the name would change according to the full rules of noun inflection in whatever language. In Latin, a noun has 6 cases, of which vocative (indicating direct address to the noun) is one.

Irish has a vocative case that can modify names, and is an official language of a UN member state.