Thanes

The experts tell me that the word 'thane' (as in "All hail, Macbeth! hail to thee, thane of Glamis!/All hail, Macbeth, hail to thee, thane of Cawdor!") is an anglicisation of the Gaelic word "Taoiseach". But I don't see that at all. The two words have no phonemes in common at all; not an initial 't' (T/TH), not a vowel (AY/EE and OH), not a consonant (N/SH and K). How would you possibly get from one to the other?

Unless it's an obscure English joke ...