Sounds like you're doing everything according to the book, although there may be a little confusion over the account. If the account is in your name, then how do you quantify how much you are actually giving your ex in maintenance? It may be better to simply pay your ex a certain amount of money as agreed, but if this is working for you and is amicable, there's probably no reason to change it, unless one of the below circumstances applies.
Depending on who the baby lives with most of the time, either one of you can claim an increase in your social welfare payment for the child.
I'm presuming you're on the Back to Work Enterprise Allowance. If that's the case, there's no need for you to tell social welfare about any maintenance paid, as it is a non-means tested payment. Your ex's payment on BTEA is also not means tested, so she won't have any obligation to advise them of the maintenance being received either, unless she is also receiving rent supplement. Maintenance by her received WILL affect her rent supplement.
If your ex was to start work, and come off all social welfare payments, then the maintenance that you're paying could entitle you to an increase in your payment for the child, even if the child isn't living with you.
If child is living partially with you, you may also be entitled to a lone parent tax credit which could help reduce your tax bill at the end of the year. This applies regardless of who the child is considered to be living with for social welfare purposes.