@Aegis 

But Italki allows us to change the name, doesn't it? So that's the " right " I am talking about. We're teachers but also users and sometimes even students of other teachers. And the message was just an idea because it'd work. I could also suggest you to take a look at the video of the teacher, that'd help you remember, but there's the possibility of the teacher deleting it or making another one without showing hi/her face, anyway, no matter what suggestions, there'll always be a " but ".. another suggestion is: block the teacher you didn't like, but then he or she could create another teacher profile (which doesn't happen very often) but again, it's a " but "...  apparently you're looking for a very personal website designed for you hehe.

Every user already has a unique italki user number, which is how you can identify them. It is shown in the session information as well as other places. I’ve never changed my italki name, and I’m not aware of any other teachers who are doing this. It seems to me that it would be counter-productive.

Teachers don’t have “avatars” — photos must be realistic depictions of the teacher, and are approved by italki. As people have a natural tendency to change over time, it makes perfect sense for teachers to update their photos from time to time. Teachers are also required to have videos, so failure to recognize a teacher would seem to be a bit far-fetched.

As the original poster recognizes, most students just try out a few teachers and quickly settle on a few they like — his habit of using a new teacher every day of the week, while apparently a good strategy for him, is not what most students are into. Teachers, on the other hand, generally deal with many lessons every day from many students, including inexpensive trial lessons, so the more likely scenario by far would be for a student to change his name and avatar (perhaps to a bowl of fruit) and request a session from a teacher who doesn’t really want to deal with him (for whatever reason).

Haha, of course we should have this very simple right. And there's nothing better than communication! If you're in doubt, just ask. That's why it's important also to send a message to the teacher at first because that will be saved in the history. 

@Christina - I agree that if italki provided a better way to identify teachers, for example, show our history with the teacher when we mouseover, then this wouldn't be a problem. They used to automatically make teachers I'd booked a favorite, so the little heart under the avatar was orange if I'd used that teacher before. That's not as nice as showing history, but it helped. Now they don't do it, which is a shame.

@Murillo Costa - Many sites don't allow us to change our user names, so why do you consider this to be a "right"? Having to write a note to a teacher before taking a lesson to see if I'd used her before would be both time consuming and awkward. I admit it's a possible solution, but it's even less convenient than looking through my long list of teachers. 

I think they should be able to. They may share the same name with 10 other teachers, they may need to comply with new italki rules etc.

Italki must provide a way to know f you have hired someone before or a way to filter teachers you didn't like instead of having to check them one by one.