How to synchronise multiple RESTFul requests when using NodeJS and saving to MongoDB?

You should consider setting the user_name to be unique in the Schema. That would ensure that the user_name stays unique even if simultaneous requests are made to set an identical user name.

Yes, the reason this is happening is as you suspected because multiple requests can execute the code simultaneously and therefore the User.fineOne can return false multiple times. Incidentally this can happen with other stacks as well, even ones that use one thread per request.

To solve this, you need a way to somehow either control that just one user is being worked on at the time, you can accomplish this by adding all registerUser requests to a queue and then pulling them off the queue one by one and calling res.Send only after it's processed form the queue.

Alternatively, maybe you can keep a local array of user names, and each time a new request comes in and check the array if it's already there. If it isn't add it to the array and work on it. If it is in the array, send the response "User exists". Then, once the user has been successfully created, you can remove it from that array. (I haven't thought this one through 100% but I think it should work as well.)