Worth checking the premise before you spend any energy on the Norwegian-entity route, because I think the split is not where it looks.
Shopify’s local payment methods page keys eligibility to where the customer is, not where the store is registered. MobilePay is described as available to customers in Denmark or Finland. So your DK store shows it because your buyers sit in DK and FI, not because the store itself is Danish. Registering an entity in Norway would not change that axis.
The real reason you cannot find Vipps is that it is not on that list at all. The methods there are Klarna, MobilePay, Swish, TWINT, BLIK, MB WAY, Bancontact, iDEAL/Wero, EPS, Przelewy24, ACH Direct Debit, Multibanco and Sofort. Vipps is absent for every store country, not just yours. Same parent company, still a separate rail, and Shopify Payments has only picked up one of the two brands so far. Good thing to know before anyone opens a NO company on the assumption it unlocks the checkout.
There is an official route though. Vipps MobilePay’s own developer docs point at a Shopify app, built and maintained by Crude, and it runs as its own payment method next to Shopify Payments rather than replacing it. Capture and refund stay in the Shopify admin. Two limitations they state themselves, worth knowing up front. Express checkout is not supported on Shopify, which they attribute to a limitation on Shopify’s side, so you get Vipps in the regular checkout but not as a one-tap button on the product page. And after you sign up you wait one to two days for the business portal login before you can pull API credentials, so it is not a same-afternoon job.
One thing I could not verify and would ask them directly before installing anything. Whether the Vipps agreement accepts a merchant registered in Denmark, or whether onboarding wants a Norwegian organisation number. The brand is shared but the contracting side may not be, and that question decides whether this path exists for you at all. Cheaper to ask Vipps sales than to find out three steps in.
How much of your volume is actually Norwegian right now? If it is a thin slice, the third-party fee and the extra reconciliation may eat the conversion lift, and that changes the answer.