No, if all the data you keep around from EU visitors is strictly for the conduction of business or a legal requirement (taxes for example) then you don't need t

No, if all the data you keep around from EU visitors is strictly for the conduction of business or a legal requirement (taxes for example) then you don't need to do anything (maybe add a text that you do save these things for business purposes). Once the data is no longer needed you should delete it within a certain timeframe (a month or so). If you save data beyond what is strictly necessary to conduct business, like doing analytics, then you will need to ask your EU users if they are OK with that. If you don't want to do that you can simply exclude EU users from any analytics.