It sounds like you are talking about a tilnavn. See https://www.wikitree.com/wiki/Space:Project_Denmark_Discussion_Draft_for_Danish_Names
Project Denmark has not yet had a thorough discussion about where to put which parts of Danish names. Some of it depends on time and the timing of Danish naming laws. See the discussion draft for when the laws changed.
But here is my best guess (before our discussion, decision and settlement on guidelines). Tilnavn are most likely to wind up being put in the nickname field when they are used as tilnavn. If it can be determined that someone actually formally adopted a tilnavn as his slægtsnavn at some time after birth and stuck with it until death, it will likely wind up being put in the current last name field. If it can be determined that someone actually formally adopted a tilnavn as his slægtsnavn at some time after birth and later changed it, it will likely wind up being put in the other last name field.
Do you have your grandfather's baptismal record? If so, how is his father named and what is the date. If your grandfather was born between 1856 and 1904, by law, his slægtsnavn (last name) at birth was frozen to be the same as his father's patronymic which would be something ending in sen. If your grandfather was born in 1904 or later, then you have a little more searching to do.
in 1904, a new slægtsnavn law was passed. People were allowed to change their slægtsnavn name to a name of their choice based on a tilnavn or by-name of a parent or grandparent, or on a place name of property or lands owned by the family for at least two generations. Your grandfather's last name would still be the same as your greatgrandfather's slægtsnavn because slægtsnavn were heritable at that time. But your great grandfather might have changed his slægtsnavn in response to this law making your grandfather's last name seem to be different. If you have the baptismal record from the church ledgers, it will list your grandfather's given and last name at birth.
Then you need to look at how your grandfather appears in the censuses, how his name appears in his marriage record and how his name appears in the baptismal records of his children and how his name appears in this death/burial record. His marriage and death records and the census will help you decide if he actually changed his slægtsnavn. If you only see the changes in the mention of him in his children's records or as a witness in other records, it is more likely the changes remained tilnavn.
Dalum and Suldrup are both place name type.
The trick is figuring out whether your grandfather ever adopted these tilnavn as his slægtsnavn or just continued to use them as tilnavn. The fact that they changed over time makes it more likely that these remained tilnavn type names and referred to where he lived at the time when they were used. Does that theory fit the known facts?