A June and a -teenth is no harder to envision than a Frapp and a CCino. It's a silly tangent.
Picturing a frappe and cappuccino gives you a sense for what a Frappuccino _is_. Picturing june and thirteenth/nineteenth only gives you sense for _when_ it is.
In only contend a better name would be one where the name suggests something about the content to someone hearing it for the first time.
They don’t even give you a sense for _when_ they are. Or, more accurately, they give you the _wrong_ sense for when they are by name alone.
Heck, Juneteenth is a better name, since it is not literally month+day.