Road names can be quickly changed by changing the name tag. This example uses a road found that does not follow the OpenStreetMap conventions of not abbreviating road names (more found here: Names - OpenStreetMap Wiki)
The same process of modifying road names can be used in various scenarios including adding, changing, and correcting a road name. This example uses Murdoch Circuit in Acacia Ridge.
With the road segment you need to modify selected, go to the Edit feature panel, at the bottom of the panel, in the Tags pane.
The tag we will focus on is name=Murdoch Cct with should be changed to Murdoch Circuit.
Murdoch Cct is above the correctly named Murdoch Circuit
name=name of the road is the focus of this example
Change the name of the road by removing Murdoch Cct and adding Murdoch Circuit. Save the edit and add a changeset comment.
The changeset for this example can be found here: Changeset: 173342892 | OpenStreetMap