The built-in feature is aptly referred to as hover or hovers.
For example, the docs for the built-in Go to Definition mentions it as:
If you press Ctrl and hover over a symbol, a preview of the declaration will appear
It is also mentioned in various language-specific features, such as this one for HTML Hover:
Hover
Move the mouse over HTML tags or embedded styles and JavaScript to get more information on the symbol under the cursor.

The relevant built-in settings are grouped by *.hover.*, such as:
// Prefer showing hovers above the line, if there's space.
"editor.hover.above": true,
// Controls the delay in milliseconds after which the hover is shown.
"editor.hover.delay": 300,
// Controls whether the hover is shown.
"editor.hover.enabled": true,
...
// Show tag and attribute documentation in hover.
"html.hover.documentation": true,
// Show references to MDN in hover.
"html.hover.references": true,
...
The contents however depend on the language of the file (as indicated on the status bar on the lower right of VS Code) and/or the extensions you have installed. For example, you said "shows where the function is defined", but for my Python workspaces, they typically just show the function signature and documentation:

So you would have to check both the built-in settings and the extension settings if you are looking for specific behavior/contents of the hover popup.
The way for extensions to modify the hover behavior/contents is also referred to as Show Hovers, and so it makes sense for extension-specific settings to refer to it as hover as well:
Show Hovers
Hovers show information about the symbol/object that's below the mouse
cursor. This is usually the type of the symbol and a description.
