While implementation is probably spotty, it is a legal requirement of the Schengen treaty that hotels verify and record the identity and nationality of all their guests. In practice this means passport, EU/EEA driver's licence, or EU/EEA national identity card must be shown on check-in.

Some EU states have even stricter requirements, such as Italy where this information must be reported to police nightly; some hotels insist on holding on to your passport overnight for this reason, causing some understandable discomfort among some.

As for data security, someone's full name and birthdate is critical vital information that is used all the time for nefarious purposes. But I would not worry about people getting this information from your passport. In some US states, this information is a public record, making it next to useless as "secrets"