Specifically, they ask how you know the person who is taking the class is the one who signed up. Faculty who have taught online report that if someone wanted to assume another's identity and take the entire course, there would be no way of knowing that. But they also point out that if Bill walked into your classroom and said he was Sam and came to every class, there also would be no way to know that.
Faculty do worry about cheating, both in online classes and onground.
Have links to sites which clearly describe plagiarism and show students how to cite correctly when they use other's words or ideas. Faculty, who have students write weekly, comment that they know their online students and their work very well, in some cases better than they know their onground students. If students write continually, it makes it easy to spot the occasion when someone else might have written something for them. Use multiple choice, short answer, and matching tests for ungraded self-assessment. These tests are easy to create in most course management systems, but hard to monitor.