Go carefully. I switched from Eir to Sky. Followed the protocol re notice etc. I was due a refund from Eir which I received. However the following month I received a text message that they were going to put through the usual monthly direct debit. I phoned them, they agreed it was a mistake and would cancel the direct debit. However as a safeguard I phoned AIB and cancelled direct debits from EIR.
Eir attempted to put through the DD. It was returned. Within 5 days, I had a debt collector on their behalf hounding me by phone. Eventually, it was sorted out,but it was very annoying.