The legislation states that an economic operator established in the customs territory of the Union shall register with the customs authority in the place in which they are established. Where an economic operator is established outside of the customs territory of the Union they shall register with the customs authority responsible for the place where they first lodge a declaration or apply for a decision.
In the event that a person applies for an EORI in Denmark but finds themselves in a situation where they do not lodge their first declaration in Denmark, but Germany, then the Danish EORI would not be refused. EORIs issued by a member State are accepted throughout the EU.
You can find more information on EU EORI here:
EC Taxation and Customs Union