That's generally the same in Danish, although one historical tidbit to add to it is that the aa->å respelling in Danish happened only in 1948. With that spelling reform, all normal words using 'aa' as a digraph were respelled to use 'å', so for example "cemetery" went from "kirkegaard" to "kirkegård". The latter is now the standard spelling, and "kirkegaard" would only be accepted in situations where it's a technical necessity (e.g. using 7-bit ASCII).
If that had been done across the board, Danish would be easy to sort, since the only digraph would have been eliminated, replaced with an atomic character. However the reform was not made mandatory for personal names; people could choose to retain the 'aa' or switch to 'å', and many retained the traditional spelling (the traditional spelling was also retained for historical figures). There was some discussion about officially reforming the names of cities to use the new 'å' spellings, but both Aarhus and Aalborg (the 2nd- and 3rd-largest cities) strongly objected. So placenames were not reformed (unless a specific locality opted in). You do occasionally see the spellings Århus and Ålborg, especially in writing closer to the time of the reform, but those spellings didn't catch on.
Actually, Århus changed its name immediately after the reform, but Aalborg did not. It was not until 2012 that Århus decided to change its name back to »Aarhus« to become 'easier to spell internationally' (which was the argument).
I still spell it Århus to taunt the idea that it was the »å« that prevented Århus from the same business opportunities as Copenhagen -- I'm sorry, København.
If that had been done across the board, Danish would be easy to sort, since the only digraph would have been eliminated, replaced with an atomic character. However the reform was not made mandatory for personal names; people could choose to retain the 'aa' or switch to 'å', and many retained the traditional spelling (the traditional spelling was also retained for historical figures). There was some discussion about officially reforming the names of cities to use the new 'å' spellings, but both Aarhus and Aalborg (the 2nd- and 3rd-largest cities) strongly objected. So placenames were not reformed (unless a specific locality opted in). You do occasionally see the spellings Århus and Ålborg, especially in writing closer to the time of the reform, but those spellings didn't catch on.