Well, the simple act of marriage does not change a person's surname. You actually have to apply for that change. It can be an expensive, laborious process -- and that alone can stop people from doing it.
I personally don't believe Kono ever did.
In the first place, she must want to keep the royal name Kalakaua. It's extremely prestigious in Hawai'i. By contrast, Noshimuri is established as being effectively synonymous with the Yakuza crime family. So on that very simple level, I highly doubt she wanted to change her name, or that Adam would have particularly pushed her to do it.
But then there's the fact that she's a semi-celebrity surfer, even years after her career ended. There are shots in several episodes where she's casually at the beach on the North Shore, and random surfers come up to give her props. She's remembered as "Kono Kalakaua", which is -- let's face it -- one of the best names a Hawai'i-based surfer could ever have.
And then there's the matter of what it would actually take for her to make the legal name change. She probably has (dozens?) of gun licenses, not to mention whatever police certifications, vehicle registrations, passports, credit cards and various drivers licenses she holds. Granted, Adam is rich, but Kono's very busy. And let's not forget how much her honeymoon sucked. She never had time to actually file for the name changes. She went directly from her wedding to the ordeal that resulted in Adam going to jail.
And then there's the behind-the-scenes rationale for keeping her name as it was. This is a legacy character from the 1968 version of the show, so the producers likely feel it's important to keep the name intact.
