What does Wren mean?
A nature name taken directly from the English word for the small, energetic songbird, from Old English 'wrenna'. It also exists as an English surname. Its use as a first name is modern.
What does Oakley mean?
A surname and place name from Old English 'ac' (oak) + 'leah' (woodland clearing or meadow), so literally 'the oak clearing'. It names numerous English villages (in Bedfordshire, Hampshire, Kent and elsewhere) and only became common as a given name recently.