Rakuten bank transfer issue due to wrong sender name (依頼人名)

Having an odd issue when attempted a Rakuten bank transfer via the app.

A store I regularly shop at is old-school, and only takes payment via bank transfer. I usually used my WISE card to pay them, but tried to do this from my Rakuten bank for the first time last week , and I was asked for (what I assume) is my own name when setting it up (依頼人名).

I rushed through it and my iPhone autocorrected (or more likely I messed up), causing a typo. The money left my account, however the shop says they've not received anything (their details were totally correct).
However the money didn't bounce back to my account or get refunded or anything. Its been a week and the store wants their money; understandably.

Any ideas on what to do next is appreciated. My spoken Japanese isn't quite good enough to explain all this over the phone to their support agent.

by No-Jello-9512