I hope one of the expert researchers in this forum will help you, as I do not know the meaning of that word.
I presume you know it is common naming practice in earlier generations for a Danish person to have both a patronymic surname and another identifying surname (place name, occupation name, etc.).
I found it interesting that this woman, below, is called Schousdatter; she lives in Skiffard village, Tøstrup parish, Djurs Nørre herred, Randers amt, Denmark. Most often we see Schou as a surname rather than a first name (as with her father).
It may not be possible to pinpoint the precise earliest use of Schou in your family (albeit the researchers in this forum are amazing). The patronymic name could stand alone and an identifier name could stand alone or both could be used together. Thus the name might not show up in written records at its earliest use.
I am quite sure others will correct my errors in this explanation if any and look forward to stopping back and continuing my own learning about Danish family history!
1845 Danish Census
Randers, Djurs Nørre, Tøstrup, Skiffard by,
Christian Hansen 32 Smed og huusfæster born in Tøstrup sogn (parish)
Kirsten Schousdatter 28 born in Veilby, Randers amt
Hans Christian Christiansen 5
Ane Mette Christiansen 3
Maren Christiansen 1
+ one apprentice smed (blacksmith)