

If "Moore Avenue" is the proper name then the name tag should just read "Moore Avenue" and the old name can be recorded as `old_name=Piper Lane`. If it is officially "Piper Lane" but is just called "Moore Lane" by locals then "Moore Lane" can be set as `loc_name`. If this changes partway down the road then it should be split at the correct point and the individual bits named separately.

For more detail see: https://wiki.openstreetmap.org/wiki/Names