Conversation so far:
Who did the invite?
At the invitation of new member Steve Wickham, Mike Scott.
What did they do?
moved to Dublin.
What happened to these men?
quickly became influenced by the traditional Irish music.
What did this?
well as by country and gospel.
What changed?
The band's line-up changed once again with.
Who else joined the band?
Wickham and Thistlethwaite now joined by Trevor Hutchinson on bass and Peter McKinney on drums.
The new band, which the official Waterboys.
What happened to the band?
Dublin and touring the UK, Ireland, Europe and Israel.

Question: What are they called?
Self-contained rewrite: What are  The Waterboys called