Each outliner area has individual selection (blue highlight).

But only one active collection as seen below (gray highlight on icon).

If you press F2 in any one area, it renames the active selection in the area where your mouse is on.

But if you create an object, it will always be created under the active collection.

If you want to rename a collection using python use any one of these:

bpy.data.collections[0].name = "new_name"
bpy.data.collections['current_name'].name = "new_name"

Each outliner area has individual selection (blue highlight).

But only one active collection as seen below (gray highlight on icon).

If you press F2 in any one area, it renames the active selection in the area where your mouse is on. But if you create an object, it will always be created under the active collection.

The bpy.ops.outliner.item_activate(extend=False, extend_range=False, deselect_all=False) operator internally uses mouse position to select and activate items.

Also there is no active_item like attribute associated with the OUTLINER space you can use.

So you can't use python to manipulate active selection in the OUTLINER.

However you can use bpy.data.collections to modify collection properties.

Please do tell what you cannot achieve without that selection.

If you want to rename a collection using python use any one of these:

bpy.data.collections[0].name = "new_name"
bpy.data.collections['current_name'].name = "new_name"