Just married! Name change on work visa?

I am American and my husband is Canadian. We've been living in Japan for several years, and this summer we got married in Canada. I read that if I want to change my name, then I need to get an entirely new US Passport. I understand that, but here's my question:
What happens to my current work visa and my multiple re-entry permit. I have a work visa that is good for another 2 years and a re-entry permit that is good for the same. Will I just lose these and have to start the visa and re-entry process all over again if I get a new passport? Will I have to pay for these stamps all over again? I appreciate any information you can share. Thanks!

What happens to my current work visa and my multiple re-entry permit.

You can have them transferred to your new passport or just continue carrying around your canceled passport together with your new passport. That is what I did for over a year.

In either case, I assume that US citizens can keep their canceled passports after cancellation. If that is not the case, you will have to consult with the Japanese immigration authorities about how to transfer your "status of residence" and "re-entry permit" sticker to your new passport. The "visa" sticker, by the way, is not needed anymore. It is only needed on your initial entry to Japan.

Thanks, Uji. In the US, we can keep our canceled passports. (They make nice souvenirs.) That means I could continue to carry both passports. When you said that the status and re-entry permit would be transfered to my new passport, did you mean that I could get them physically put into my new passport for free, or that the rights that go along with them would be tranfered as long as I have both passports in hand? Just clarifying. I really appreciate your response.

When I got my new passport I went down to the Immigration office and it was avery quick process for them to put new stickers in my passport. You then also have to go to your ward/city office to update your alien registration card with both the name change and the new passport details.