Whether print or digital media, what is the name of this element?
On the main page layout, there is a small, not too obtrusive element with text inside. Usually a circle. It's not a callout because it's not referring to anything specifically on the main layout.
Here are two examples. See top right hand corner.
Callout is what I generally refer to them as. A call out doesn't necessarily have to be literal. It can "call out to the viewer" not merely "call existing content to the foreground".
Clients can refer to them as "badges" or "seals" or "bursts".
In terms of design, then can also be referred to as "bastards" or "bastard elements" at times. By nature they are meant to be different than the rest of the design to call attention to themselves.
I've not come across a standard term for these. They've been variously referred to as "splash," "screech" and "decal" in conversation with different designers over the years.