Danish surnames always ends with -sen. My surname is Nielsen. If I had been Swedish it would probably have been Nielson. Rich or poor - that's how it is. However, if you were a descendant of a foreigner - a Scandinavian - you might bring it into your Danish family.
Earlier a male would be called a sen-name after his father and a female -datter after her father. But they would be born in the early 1800.
The name Elizabeth could occur in DK. But mostly it is Elisabeth. Danes at that time liked to find foreign names for their children. Lately I have found two female family members christned Indiana. They were from early and middle 1800.
Greetings Jette in DK