Dynamically populate the menu when a new category is created

I was asked to make a dynamic menu with sub-items. This is the idea:

$categories = array{
‘cars’,
‘boats’,
‘airplanes’
};

On the Categories session, I’ll place an array dynamically populated with all categories.
And… The most important part… Every time a new category is added by the user, a
new sub-item must be added automatically.

Is it possible to do it?