Bubble hat or beret?

[Ookoo]

When I purchased this hat, it was creased and flattened and described as a military style beret.

But when I poof out the creases, it looks more like a bubble hat:

This is what it looks like inside:

The label says "Adolfo II New York Paris"

The stamp says "Martelle Body made in West Germany"

So, is it a bubble hat or a beret?

 

[MyVintageCocktail]

That is SO cute! I'd sure call it a bubble hat--I can't imagine it being, or being called, a beret with that wide upswept button trim. I've had "bubble berets," but your hat looks much taller, so I would call it a hat and not a beret. It doesn't look like it's supposed to have a dented crown. I supposes someone could wear it like that if they wished, but even with a dent, which does sort of give it a "military look," but I still wouldn't call it a beret!

I would steam it lightly and stuff with soft white tissue, or put it on a head form (stuffed with tissue in the crown if needed) to smooth/reshape it.