After you update your ARC to the new UI format (one letter nine numbers) there are a certain number of other agencies you need to update information with, as cross-ministry communication does not seem to have been very broad:

1. If you have a work permit (APRC holders/students with internships or part-time jobs) you NEED to apply to the Work Development Agency for a new one. You can apply online through this system, or use the form available at the office (or here), a photocopy of it, a one inch photo, a copy of both sides of your OLD and NEW ARC/APRC and a copy of your passport.

(NOTE/UPDATE: I previously posted that you needed to hand in NT$100 or a postal order of an equivalent amount, as this is what they told me over the phone, but when I received my new work permit, it had a letter attached saying that the NT$100 postal order that the person on the phone had insisted was necessary, was not required, along with a complex form on how to get this money refunded.)

If you want to go in person and are registered in Taipei, the address is:
10F, No. 39 Zhonghua Road Section 1, Zhongzheng District, Taipei City 10042
10042 台北市中正區中華路一段 39 號 10 樓

This is also where you post your material.

2. You or your employer should fill out the form here to ensure your labour insurance contributions are still registered to the same person, one copy should be sent to the Ministry of Labour (勞動部勞工保險局，臺北市中正區羅斯福路一段4號) and the other should be forwarded to the National Health Insurance Bureau in your region (see form for addresses). Despite the claims that you don’t have to update your NHI card, I don’t really see how this is going to be possible, given that on the bottom of the form it says that your original NHI card will be cancelled when the new data is received, hence:

3. NHI card renewal (purportedly optional): This is relatively pain-free, simply go to the Post Office and ask to renew your NHI card, with your ARC and a photocopy of both sides, one photograph (most machines have a special setting for NHI card photos) and NT$200. You should receive your new card in 5 working days. And after you receive it, you can switch your NHI app card to the new one.

4. Alien Digital Certificate: You can apply to update this at the same time as you apply for the new UI format, with the same material and you shouldn’t be charged.

5. If you have a post office account, you have to inform them of your change of ID.

Other issues: Despite assurances that banks would be automatically informed of changes, people on Facebook have been describing demands to close and reopen accounts at banks, issues with motorcycle licenses/test applications, property deeds, mortgages, car loans. With hospital appointments, many clinics and hospitals will still have your old number in their systems, even though with your new NHI card, doctors should still be able to access your previous publicly held records.

UPDATE (March 9, 2021): My ESun Wallet app stopped working today and displayed a message that I needed to re-register as my details had recently changed. I did this in the space of about 30 seconds and there was no problem. My account and cards were still registered on the app. My banking app on the phone and the internet also stopped working and I had to re-apply for internet and mobile banking.

The steps are easy enough, but you must apply again for internet banking:

You will be asked to enter your email, your new ARC number and your date of birth. Then you have the option of an audio OTP call (in Chinese) or some other options. Once you’ve confirmed, you have to set a new username and password and either confirm the changes or login. If you have a savings account and a credit card, you just need to use the savings account option and the credit card information will follow.

Once you’ve reapplied for internet banking and logged in, you MUST log out of internet banking before you can log in to your mobile app using the same details. You’ll have to agree to terms and conditions again, but it’s reasonably simple.

UPDATE (April 16, 2021): Today, one of my four other banks informed me via text that they had received the update to my ARC number:

As I’ve only got a credit card with them and no bank account, they didn’t use my ARC number as the identification number for my account, so the only thing I had to do was re-log into my mobile credit card app:

UPDATE (August 8, 2021): Megabank sent out a mailer to all its clients telling them to update their info with the bank. As opposed the easy methods provided by the banks above, they decided that you have to mail the form (with the information that they already have) to your branch (they say any branch, but I have my doubts) or go in person. After a long phone conversation, I ended up mailing the details, and without notice, they changed the login details on my phone without informing me. If you get a message a few days after informing them of your new ARC/APRC number, just try logging into the app with the new number and you’ll be able to get in. But there’s a problem with your 「行動安全碼」 mobile banking number and your mobile phone will still be associated with the old account number for some reason. To re-tie your account to your mobile device, you have to uninstall the app and then reinstall and log in again. Then you go to the main menu (選單） and hit settings (設定） and you should be able to apply for a new mobile banking safety number by filling in your ARC number (the new one) and your passport number. Bizarrely for me, even though I’d provided them with my new passport number when updating my details, I had to fill in my old passport number for it to work.

The remaining two banks are yet to notify me or make any changes, but will update when they do.

UPDATE (March 22, 2021): My doctor had pre-booked me in for an appointment before “the change”. I turned up for the appointment expecting for there to be a little confusion but for things to be sorted out quite quickly when they saw the old number on the back of my APRC. In fact, I needed to go back to reception and reregister my old details to the new card and then reapply for an appointment. There were no more free spots on the day in question, however. Luckily for me the pleasant and slightly frazzled lady at the counter decided to help me out and scribbled a hand written note to the doctor asking that I be added manually by the doctor to the list of patients. This was nice of them, but it’s unfortunate that there has been no effort by the government to inform staff at hospitals that this is going to be an ever more common scenario.
FURTHER UPDATE (August 2, 2021): I’m not sure if the lady I mentioned above was overly frazzled, as when I went to the hospital where this happened to get my vaccine, they printed out a form which had me listed as a woman and had my (male) friend’s phone number as the contact number.

UPDATE (April 9, 2021): A reader has outlined the requirements for Drivers’ license updates:
Just go to the local Department of motor vehicles and bring two photos and NT$200 for each license you hold.

I have to say I’m yet to find anything easier because of the new format. Please do let me know if there are any benefits to the new format.

Shout out to Slawa who made this call for names of websites where the new ID number does not work towards the end of last year and for driver license info.

If you have more specific queries about particular ministries, I suggest having a look at the Q &A on this page.

Remember to reregister for the EZ Way app with your new ARC (note, real name authorization is now available for foreign residents.

Bonus reading: This foreign resident doctor lists his own complaints, which extend to the cancellation of automated credit card bill payments, the requirement to replace his medical license and Examination Yuan license, amongst others.