I can't speak for Italy, but on numerous overnight trips between France, Austria, Germany and Netherlands (and Czech, Slovakia, Poland, etc) in recent years, I haven't once been asked by train staff to show my passport (unless I was using it as ID for an online ticket), let alone hand it over. However, as Togo says, there can still be 'random' police checks, when they will ask to see your passport (fortunately, I've only had this in the evening/morning, not in the middle of the night...)

In France, Germany and Netherlands, I haven't been asked to hand my ticket over either - although in Austria (and Czech, Slovakia, Poland) you may still be asked to leave your ticket with the conductor overnight. I normally travel on self-printed online tickets, and carry at least one spare - so I have no hesitation about giving a copy to the conductor if they request it. I can understand you may be more hesitant letting an Interrail pass out of your sight, but as adventureadam says, these are professional staff, so it shouldn't be a problem (just don't forget to collect it again before you get off in the morning!)

It's true that most regular tickets purchased offline don't include a name, but I thought Interrail passes included the passenger's name?

My night-train memory, 2014 timetable:
CNL418, R440, EN445, CNL456, CNL457, CNL1318, CNL1319