With Search Customer invocable action, you can search customer in Stripe by name and/or email. You can automate customer id mapping from stripe to Salesforce by simply adding it in your Salesforce Flow, and then map the Customer Id from response to your choice of Salesforce object's field accordingly. Basically you would pass few parameters i.e. Payment Record Id (Lite Pae Payment Record), Customer Name or Email or both (AND operation), Create if not found (optional - if you want to create new customer in Stripe if none found).

• Create a new flow.
• Add logic to have Customer Name or Email.
• Add a step to query Payment Account and store its Id in a flow variable i.e. paymentRecordId.
• Add a new Action and search for Search Customer.
  • Setup its input values based on previous steps like paymentRecordId, Customer Name, Customer Email,Create If not found, Log error.
  • You may want to handle its reponse as well to output variables by clicking on Advanced section of this node. Specially, Customer Id.
• You can add a screen component to show the reponse from previous step.
• Publish flow.
• Add this flow on your Salesforce Lightning page, Experience Cloud Site or any scheduled automated processes based on if you have any screen component on this flow.