"Thank you, Finlay"
Translation:Tapadh leat, Fhionnlaigh
If Fhionnlaigh started with a consonant – yes. But this a disappears before vowels and Fhionnlaigh starts with a vowel (notice that lenited fh is silent).
See how similarly a changes to an in English before vowels, even though the word is written with a silent consonantal sign in the beginning, eg. an honour.