Should I Let My Child Be Wrong?

My ten years old daughter had attended a workshop and when asked what is her mom’s occupation, she said ‘Psychologist.’
I am NOT a licensed psychologist. I am a life coach.
When she came home and told me that, she said she is embarrassed to say that her mom is a coach, because that some made-up unreal job.

I told her that this made-up unreal job generates six figures to our home, affording us to live comfortably and for her to have everything she wants.
I continued by telling her that I make real impact on people’s lives for the better and that I am very proud of myself.

Being the almost teen that she is, she said, ‘It’s okay as long as you and your clients believe that. I would feel much more proud if you were a licensed psychologist.’

I would have preferred if she thought differently about what I do, but even though she is not an adult yet, I guess she gets to think whatever she wants.
Still, there is a weird feeling I have now, knowing that this is what she thinks of what I do.

Should I even bother trying to change her belief or should I let her be wrong about me?