Hi! You're asking Flemming about his comment and he'll have an answer but I hope you don't mind me chiming in as well. Quick answer is - no, Peder just did a normal Danish thing to do, that's all. Throughout the 1800s Danes passed laws encouraging people to leave the patronymic naming system behind and adopt permanent surnames. (Patronymic names as you know are based on the father's first name + sen or + datter; permanent surnames are what Americans use, a last name that is passed along). Yet customs held strong, and thus this was a long, gradual transition. In 1904 a new law about naming spurred a spate of name changes, with many people choosing a permanent surname for themselves and their descendants. By choosing "Holbæk," Peder was modernizing his family and also conforming to Danish law that intended him to do so.
By saying Peder "was allowed" Flemming is referring to the fact that a legal name change would have to be legally approved, as in the USA. The difference for Peder (as compared to Americans) is that the government is encouraging him to make this change. A few names were protected (a person couldn't just adopt the surname of a royal person for example) but Holbæk was an "allowed" name.
Illegitimate children were given either a patronymic name based on their father's first name OR were given the last name of their mother, depending on the situation. If the father acknowledged the child and allowed his own name to be used, his name was given (his first name + sen or + datter). Peder's father was Jørgen Pedersen, so therefore Peder's patronymic name of "Jørgen's son" probably comes from his father. The situation is a little cloudy from these many years later, since Peder's mother's last name was Jørgensdatter/Jørgensen. Just a funny coincidence, that either way, Peder would be Jørgensen. But the father is named on Peder's birth record, so I presume this is because the father didn't argue about it but instead acknowledged the child. It seems a little more likely then, that Jørgensen comes from Peder's father.
Now Flemming and/or others I hope will confirm this or correct it or add to it.
Why Peder chose "Holbæk" specifically can't be known, but you could trace where this identifier name comes from (for example, whether it was used in the family previously). It was common for a person to have first name(s), patronymic name, and then an identifier name. As an example a person might be "John Smith Policeman" or "John Smith Chicago." To my ear, "Holbæk" sounds like a place name. Certainly it was common knowledge that the nation had too many patronymic names - too many Jensens, Andersens, Petersens, Jørgensens, and the like - so Peder was typical in choosing to drop the patronymic.
More on the link below about the different types of "identifier" names:http://www.mydanishroots.com/surnames-meaning-and-origin
Many places in libraries and online to read more, such as this:http://www.danishkin.com/namingtraditions.html
My guess is that Flemming found a note about the name change in a church book. Again, a guess, I would think that the pastor would return to the birth /baptism record and add the note there. Traditionally Danes kept records in church books that Americans would keep at the county courthouse.
Hope this helps. :D
P.S. there's a place called "Holbekhuus" in Hindsted herred, Aalborg amt. And a database called "krabsens" is a good spot to look up place names.