It's called the foot — the thing that goes into a shoe. You can find this in [ISO 518:2006], the standard which describes the... standard... hot shoe. It's not, however, defined there — it's just basically used as if everyone knows what it means. (Which, I guess, we do.)

The dimensions given in Figures 1 and 2 are basic for the solid shoe. When an accessory shoe is equipped with springs or other devices for holding the accessory foot tightly or maintaining good electrical contact, the dimensions of the shoe can be changed within the range in which their interchangeability and functions will not be affected.

(Emphasis added.) We can see here that they use "accessory foot"; things like "flash foot" also make sense when the accessory is in fact a flash. I've also seen the term "ISO foot" — a flash or accessory foot which matches this standard.