Seeing as in this scenario the three buttons all related to the same type of action, there is no problem with using a status-dependent button text.
It would help the user to label the button with something that gives a clue as to what it manipulates, i.e. Connection and the button then gives the action you can apply to the connection.
Additionally you could or should signal the change in button action to the user somehow. This could be fade the button out and then in with different text, or somehow highlight the button while the text changes, anything that make the user realize the button function changed.
The same type of approach works with forms where you have data and a button to manipulate, which, when clicked, changes into a save button. All in all, this method can actually declutter the UI, but you have to be careful not to make things incomprehendable.