Set Display Name as First Name, Last Name

This is a requirement I've had previously, and never really found a proper solution. I keep thinking I must be missing something, and surely there must be a Woordpress setting to do this.... but not found one yet!!
I have also come across this post regarding a similar issue. I'm not a coder so woudln't attempt this on my own.
I want to set the Display Name for a user to their first name + last name. I don't believe this cannot be done on the fly, as various application functions use the Display Name for instance in email communications. So ideally, when a profile is created, or updated, it the display name must be set to the First Name & Last name.
It is not a site where users are even aware that such a thing exists. In both instances where I do have this requirement, I am using the membership plugin too, and I do use the 'Profile Fields' option, but sadly, this does not feature in it!