I want to switch from Eir to Three but I can’t manage to close my Eir account. My account is on direct debit. If I simply switch to Three using the same number will Eir just close the account? Their customer service is terrible
What sort of account is it? Pay as you go? Contract/bill-pay? If you're still in a contract period then moving to another provider and porting your number over won't necessarily cause the account to be closed as you will probably still owe them money. If you're not within a contract then it may get closed automatically after you move. You probably need to persist and sort this out with Eir.
You should be able to do it online through the Three website. Or go to a Three store and they will do it for you.
Three's customer service is also terrible. Mobile phone companies want to avoid having customers talk to people as much as possible. Using @eircare on twitter is probably your best bet for any issues but that is also pretty bad.
Check your contract for the cancellation terms and conditions which should clarify what, if anything, you may still have to pay (e.g. 30 days notice) before cancelling the DD. Of course, if you're out of contract then you could just try cancelling the DD now and moving to another carrier and porting your number over. If you owe anything I'm sure that they'll let you know. Just be careful that a cancelled DD doesn't allow them to charge you any additional penalty if they present it and it fails. Best to persist and clarify these issues with their support if possible.