These payment provider icons are actually triggered by the Shopify platform rather than being under the control of the theme itself. They are based on the payment settings live on your store, but can be over-ridden if needed, as the below Advanced Guide notes:
As Shopify has now requested, all third-party theme developers now do not provide coding customisations:
As such, you would need to approach a specialist in coding customisation to add in bespoke icons, if you wanted anything other than the ones reflecting those set up in your Shopify admin area, or if you wanted to alter the order in which these are displayed:
As such, we would recommend you reach out directly to Shopify Support who would be best placed to help.
If you require further assistance or need further technical information relating to your theme after you have spoken with Shopify, please don't hesitate to get back in touch with our Support Team.