The obligation of hosts is to register all guests, and even though, we explicitly added this sentence in our rules: "All guests are asked to provide their ID upon arrival in order to be registered at the local authorities".
Regardless whether this is mandatory or not in your country, write details from their passports/IDs. To prevent fake accounts, write some rule similar to ours. In addition, before the arrival (e.g. a week), send guests a polite reminder with everything they need to know, including this one in a subtle way.
First, this is a filter that will repel those who think they can accommodate anonymously. Second, those who stay in your place will refrain from doing something you wouldn't like as you have their details.