I'm not referring to renaming but to pushing a renamed branch and to setting the tracked branch to pushed renamed one.

What is the "standard" window?

Does it allow to automatically push with the new name and does it automatically set the tracked branch to the new one?

I meant "Move Commit": Selecting one commit and moving it with the mouse to a different location within its branch. So neither cherry-pick nor rebase.

Oh, I see. But it does not always work. Maybe it's related to moving the mouse too far (it changes to a forbidden icon) and then back. Then, it almost never works. That should not make a difference.