It's been fairly common in Norway that females take their husband's last name when they marry. (There are also some males who take their wife's last name, in recent years.)
Märtha Louise renounced her HRH before the wedding, so that she could be able to work, and pay tax of her earnings.
The point is that her aunts, Princess Ragnhild and Princess Astrid were in the same situation as Märtha Louise upon their marriage - they also married commoners, and thus they lost the HRH, but King Haakon and King Olav decided that their style wouldn't be Mrs. Lorentzen and Mrs. Ferner as would have been normal. As they were princesses, their names became Princess Ragnhild, Mrs. Lorentzen and Princess Astrid, Mrs. Ferner. Princess Märtha Louise just decided to not adopt Ari's last name upon the marriage.