Disclaimer: I'm heavily involved with this project.
Rubberduck is an open-source add-in for the VBA/VB6 IDE under [very] active development, that includes this functionality.
Version 1.3 includes a Rename refactoring:

Version 2.0 (beta available, still stabilizing) includes a dozen refactorings:

- Introduce Parameter promotes a local variable to a parameter
- Introduce Field promotes a local variable to module scope
- Encapsulate Field turns a public field into a property
- Move Closer to Usage moves a field that's only used in 1 procedure, into that procedure. Or moves a local variable immediately above its first use.
- Extract Interface lets you pick what class members to extract into an interface, creates a new class modules with stubs for them, and makes the original class implement the extracted interface.
Implement Interface creates stubs for all members of an unimplemented interface, so you don't need to create them manually by selecting them one by one in the code pane dropdown:
Implements IClass1
Public Sub IClass1_DoSomething()
Err.Raise 5 'TODO implement interface member
End Sub
Public Function IClass1_GetFoo() As Integer
Err.Raise 5 'TODO implement interface member
End Function
Sub DoSomething()
End Sub
Function GetFoo() As Integer
End Function
More refactoring tools are on the project's roadmap (including Extract Method), which you can follow on GitHub.