Check for any email or documentation you may have received upon setup of your payment gateway
Also check your payments gateway setting page https://myshopify.com/admin/settings/payments
Or contact firstname.lastname@example.org directly
I have the same problem. I can not locate my Merchant ID. The solutions mentioned above did not work. I sent an email to the link provided. I received an email back saying they no longer accept emails. They provided a link to the support center where there is 24/7 support (???), but that page is blank and there is no way to contact anyone! Since the Shopify team is so difficult to reach, can anyone else point me in the right direction?