Teachers can randomly assign students to read randomly by calling them by name. The key is the order of the direction and the assignment. Here's how: "Turn in your Bible to Isaiah chapter 1. [pause] Everyone look at your scriptures. We'll be reading verses 1-15 aloud one at a time and discussing each individually. Verse one ...[pause]... John?"
The important thing is to direct everyone to the verse, pause, and then make the reading assignment. This direct and pause gets everyone to look at the material and then you make the assignment. Everyone is engaged with the material, and because they don't know who will be called on to read, they are paying attention. Now that the assignment is given, most students will follow along unconsciously because their attention has already been directed to the text.
I think this technique is best used when reading sections where you'll be discussing each verse as you move along. It's a little more serious and good for that kind of reading.
Some teachers are uncomfortable with cold-calling. Please know that cold-calling is not cruel or chastening or a negative teaching method. It's a way of helping each student engage and participate. There is an EXTENSIVE discussion of this technique on pages 111-125 of Teach Like a Champion by Doug Lemov.
In the gospel classroom, I don't use cold-calling for asking questions. I only use it for making assignments for reading or something else where it's easy for the student to participate. I also rarely use it to get someone's attention who is talking or distracted. Usually I touch that person on the shoulder and point at whomever is speaking. That's usually enough to get the person back on track without singling them out verbally.