Die Angaben des Geborenen wurden am 07.12.2009 im Geburtsregister Nr.: 1 unter der Nummer: 1712 im Personenstandsamt eingetragen.
Die Angaben des Geborenen wurden am 07.12.2009 im Geburtsregister Nr.: 1 unter der Nummer: 1712 beim Personenstandsamt eingetragen.
Is the meaning changed by using "beim Amt" instead of "im Amt"?
You can use both im and beim, but if you used im, people would assume you are referring to the building the institution is in rather than the institution itself.
It's the same with im Geburtsregister. That means it was actually written into a file. If you wrote beim Geburtsregister instead, people would assume there's an office inside the Personenstandsamt which is named Geburtsregister.
First, the office handling the "Personenstandswesen", maintaining the "Personenstandsregister", issuing "Personenstandsurkunden" is commonly called Standesamt. I wouldn't rule out that some municipality somewhere uses the term "Personenstandsamt", but that would be the exception to the rule.
Regarding your questiong, there's a little difference in nuance. "Im Amt" puts the focus a bit more on the physical office, on the building it resides in. "Beim Amt" puts the focus a bit more on the office as an abstract institution.
