Potential employers will google the names of applicants before an interview, and if the first thing that comes up is your name and photo on a story about your first job burnout, you're going to have a very difficult interview, if they don't cancel it altogether.
It depends on where you live of course, but where I live (Western Europe) a burnout on your resume can be a career death sentence. It's illegal to fire an employee who is home sick, and people unable to work because of a burnout can stay home sick for months or even years at the employer's expense.
If it happens, you try to hide it on your CV. 'Stayed home taking care of children', 'Went back to college', 'Took a sabbatical', 'wanted time to travel' even a serious but purely physical illness (that was cured), all make good excuses. If there's a hole in your CV that can't be explained in such a way, they will assume burnout, and will likely not want to take the risk.