If you want to register the first name of a newborn child, you should turn to the Swedish Tax Agency. Likewise if you want to replace, remove, add to or change the spelling of a first name. If you want to make more changes than that, you should send your application to PRV. In it you should justify why you want to make the changes. If you want to replace all your first names, you should apply to PRV.
Example of a first name change
Susanne Granström has been called Sanna all her life. She now wants to replace the name Susanne with the name Sanna. She only has one first name, so she can only add new names at the Swedish Tax Agency, as you must always keep at least one of your first names. She does not want to be called Sanna Susanne as the names are too similar and chooses instead to turn to PRV to remove the name Susanne. When she is changing her first name, she takes the opportunity to add the name Katarina, after a dear relative.