The page numbers in an InDesign index will adjust, but not automatically.
Each entry is marked on its page with an Index marker, and you have to generate a new index after any page changes.
Thank you for your quick respons SRiegel. How do I generate a new index exactly? This would save a lot of time (and errors )
In the Index panel, Generate Index will ask if you want to replace the existing one.
The index is created by adding an Index Marker for each item you want to appear in the index.