My understanding is he/she wants to do a bank deposit transfer? Like Zelle for Bank of America? You might want to ask him/she. Shopify does allow custom options.
To see this options:
1. From you Admin page, go to Settings on left hand bottom corner
2. Go to Payments, and you should see the option for custom payment. See image below
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You could. But this might interfere with the cash tracking, if you are also receiving cash.
Maybe can consider this, would this payment method be a norm (more than 1 customer will be using this?) 1. If yes, just create a custom Payment Type for easier tracking. 2. If no, then you can just use Cash this time, but just make a note somewhere.
(though either way, option 1 should be the correct way to go)