At today's Council HM The King of Sweden announced that the new-born Prince will be named Alexander Erik Hubertus Bertil and will be Duke of Södermanland.
Prince Alexander's CoA will not be made public until later, but according to normal practice it should be the royal arms with the arms of Södermanland in Q3
The previous Duke of Södermanland's CoA was different:
For those who are wondering where Södermanland is, it is the county immediately south of Stockholm (indeed much of modern Stockholm is in Södermanland).
Something else, non-Swedes need to know is that Södermanland is pronounced "Serdermanland", and more usually written Sörmland and pronounced "Sermland".