How would you write e.g. the Spanish surname Yáñez ?

Unless it's a famous person who lived several centuries ago, probably would leave it as Yáñez, or if I (or more realistically, an average, not too technical user) were to not have an easy way to input the special characters, then as Yanez. Probably not as Yánez, even though we do have the letter 'á', but leaving it as is may be more misleading in terms of pronunciation then the non-accented version.

I think that's roughly similar to how it's done in American English (though Americans are probably less likely to have any idea how to type accented letters). A serious publication would write Yáñez but an average person would be pretty likely to just type "Yanez". Anyway, my point was just that it's not too weird to see someone write "Erdos" if their native language doesn't have the ő character.