"A Danish man would have a "surname" based on his father's name + sen (such as "Ole's son"). So a Danish form would be Splansen. Could that be Svensen, or Paulsen, or...."
I should have pointed out that a patronymic name lasts only one generation. Each man who has children gives his children his own first name + sen. (in the case of daughters the older tradition was to use his first name + datter).
Thus if "Splan" is a mangling of a Danish male name, it would have to "stick" to the family as a permanent surname during the years when Danes abandoned the patronymic naming system and adopted surnames. This would be anytime over a number of years from about 1800 onward.
More likely that Splan could be based on a Danish place name (and more likely still that it is not Danish). A Dane might carry a first name, possibly a middle name, a patroymic name, and an identifier name (such as a place name or occupation name), in that order. I suppose Splan could be an occupation, etc. Read about Danish naming practices to discover all the varieties of what I'm calling an "identifier" name.
Here's an example of a place name at the end: Nicholas Mikkel Olsen Splantown. I'm just making up a silly example of "splan" appearing in a place name.
When choosing a permanent surname, Danes and other Scandinavians sometimes adopted their place name (or other identifier name) instead of their patronymic name.
So that's just background information you don't need now, but may help if you want to explore "splan" as having a possible Danish root.