What is the meaning of the name??

The name comes from Latin:
Cupa, means vessel or barrow. Cuparius means vessel-, cask- or barrel maker, what to day is called a cooper.
From lower German comes the word kuper, from upper German Küefer and later Küfer.
In other words one of the earlier ancestors must have been a cooper.
The name comes in many varieties such as Cuyper(s) Cuiper(s) Cuijper(s) Cupper(s) Cuppen Kuiper(s) Kuper(s) Kupper(s) Küpper(s) Küper(s) Kuijper(s) Küpker, but also names as Fassbinder, Büttner og Böttcherhas the same origin.

How did they end up in Denmark?

johannes Küpper was a “dugmager” in German “Tauchmacher”, some places also told to be a felt cutter. A “dugmager” is a weaver.

From the mid to the end of the 1700 a lot of German craftsmen came to Copenhagen where they worked in the clothing industry where several major clothing factories had been built.
One of this factories were placed in Blågård. In the census papers for Copenhagen in 1787 and forward one can read that a lot of the implied lived in a special part of Copenhagen called “Udenbys klædebo kvarter”.

In the book “ Kjøbenhavn, del III, kap. III af Carl Bruun (1846-99), Thiele, 1901” it is told how a, factory owner, Johan Paul Kalckberner for a sum of 32.000 Rdl. in 1780 buys a part of Blågård.
Johan came from Burgscheidt near Aachen, and had there worked in the clothing industry. “Caused of rigorous differences” he had left a merchant house and in steed turned the sight against Denmark.
One could imagine that he in connection with his wishes making a clothing factory in Denmark had found his workers in the place where he came from.
About religion Johannes Küpper was a catholic. In the arrears around Aachen there were both catholic and protestant cloth makers and between these a lot of tensions. They had split the arrear between the groups in general the Catholics were in the city of Aachen and the protestants in the surrounding area.
So far some general remarks about the name Küpper.
I up to today I have not been able to find of Johannes Küpper and Elisabeth Rey in Aachen.