Eunice here from Shopify, thanks for posting, and welcome to the Community!
This can happen and when it does, it can cause a customer a moment of panic. But fear not! There is a reason for this phenomenon:
Certain banks or card issuers, especially those issuing debit cards, sometimes have more difficulty than others displaying pending authorizations. This means that sometimes a charge will show up twice - once as a charge, and once as an authorization. This is likely what your customer is seeing, but it doesn't mean that they have been charged twice.
I recommend asking your customer to check their bank statement for two complete charges. It's good to note that mobile banking apps have difficulty in displaying authorizations accurately so it's always best for the customer to check a full desktop version of their statement or a hard copy from their bank. If the customer is not able to access their statement, they should be able to validate that their sales were not double charged by calling their bank.
If a customer says their bank shows two complete charges then please reach out to Shopify Support via the Help Center so we can investigate. For the fastest support, I always recommend the chat option.
Top tip -
As a merchant, this is a great opportunity for you to flex your empathy and customer service skills. Not only is this is a chance to resolve a problem, but also to transform someone's mindset about your brand from negative to positive through your way of handling their concerns. I recommend checking out this awesome blog by Shopify before you contact your customer to help you prepare for the conversation ahead.
I hope this helps and good luck!