The Wren is known as Drui-en or the Druid Bird in Irish Gaelic. In Welsh Dryw means both Druid and wren. In Manx Dreain from druai dryw means the Druid’s bird, which is exactly the same as the Irish Gaelic meaning. In folklore the wren is associated with lightning, which would connect it with the thunder god Taranis. Llew Llaw Gyffes wins his name by striking a wren.
From Wikipedia: “In the Isle of Man, the hunting of the wren is associated with an ancient enchantress or ‘queen of the fairies’ (or goddess) named ‘Tehi Tegi’ which translates to something like ‘beautiful gatherer’ in Brythonic (the Manx spoke Brythonic before they switched to Gaelic). Tehi Tegi was so beautiful that all the men of the Island followed her around in hope of marrying her, and neglected their homes and fields. Tehi Tegi led her suitors to the river and then drowned them. She was confronted, but turned into a wren and escaped. She was banished from the Island but returns once a year, when she is hunted.”
Interestingly Llew Llaw Gyffes figures again in Robert Graves’s The White Goddess as one of a pair of hero figures as a variant of the Holly King/Oak King pairing, Llew’s opposite being Gronw Pebr, his love rival who cheated with Bloduwedd. Other notable pairs from Graves include Lugh and Balor and Gawain and the Green Knight. See also James Frazer The Golden Bough Chapter 28 The Killing Of The Tree Spirit in the section The Battle Of Summer And Winter. A bit of a shame in some ways as these connections cast some doubt on the authenticity of this particular tradition, although it makes for a good story.