I changed App Name Display Option from Use App Name to Use Custom Name about 10 days ago, then I released a new version of the app today. However, the infomation in the App Store is not updated, and the updated info on App Store Connect are still displayed in yellow color with this text:
"We'll review the new name before we make it available on the App Store."
Do I need to submit the change to review manually? How?
No. If it wasn't submitted, you would not have been exposed to that text.
Go back and re-check all ASC forms you touched, make sure you saved at the end of any changes to them, then make a note of app/IAP status and sit on your hands. Be sure to confirm no emails from Apple are being spammed filter out of your inbox.
ASC - App Store Connect.
Any time you're making changes to an app's meta data in, IAP, etc. while logged into App Store Connect. you're working with what is basically a form...filling out blanks, checking boxes, entering numbers and text into input boxes - a virtual form. When you finish, there is usually a button to save what you entered. Saving commits it to the servers on the backend, providing information used by the processes on the backend to complete your submittal, trigger a next step, etc.
Always be sure to hit that save button after filling things out/making changes. Sounds like you did that, at least in this case, but I'm encouraging you to go back and double check.