I guess the easiest todo is to set up a map of glyph names to change...

# map the old name to a new name
glyphNameRenameMap = {
    "a": "a.new",
    "b": "b.new",
}

# get the current font
font = CurrentFont()
# start loop over all glyph names to rename
for oldName, newName in glyphNameRenameMap.items():
    font.renameGlyph(oldName, newName, renameComponents=True, renameGroups=True, renameKerning=True)

This script expects two UFOs. The CurrentFont is your source font (has the glyph name you want), the other font is your target font (where you want to change the glyph names).

# Copy glyph names from current font to other font based on index only

srcFont = CurrentFont()
fonts = AllFonts()

# Open 2 UFOs
if len(fonts) == 2:
    # Source font (srcFont) is current font
    # Target font (trgtFont) is other font
    for f in fonts:
        if f != srcFont:
            trgtFont = f

    # collecting old and new names of glyphs from
    # srcFont and trgtFont using the index of the glyph order.
    oldNameToNewName = {}
    for gNameNew in srcFont.glyphOrder:
        gNameNewIndex = srcFont.glyphOrder.index(gNameNew)
        gNameOld = trgtFont.glyphOrder[gNameNewIndex]
        # If name of glyph in srcFont and trgtFont with the same index are 
        # not the same store their names in the dictionary oldNameToNewName
        if gNameOld != gNameNew:
            oldNameToNewName[gNameNew] = gNameOld
    for newName, oldName in oldNameToNewName.items():
        print("# changing: "+oldName+" → "+newName)
        trgtFont.renameGlyph(oldName, newName, renameComponents=True, renameGroups=True, renameKerning=True)
else:
    print("# Open two UFOs")