Bigo account deleting problem

This has got to be a scam. Yet you initiated the contact, right? I'd find some other way to delete the account that's for sure.

Did you provide any potentially damaging information to anyone? If yes, you'll need to follow up, for example, with a credit card company, Apple, your bank, etc.

If you gave you Apple ID password to a scammer, then

Change your Apple ID password https://support.apple.com/en-us/HT201355

Here is What to do after you change your Apple ID or password https://support.apple.com/en-us/HT204071

Learn about Phishing, Scams, Apple Practices,etc.

 See If you see apple.com/bill, itunes.com/bill, or an unfamiliar charge on your statement https://support.apple.com/en-us/HT201382

See Identify legitimate emails from the App Store or iTunes Store https://support.apple.com/en-us/HT201679

See How to avoid scams when using Apple Pay to send and receive money https://support.apple.com/en-us/HT208226

For scam related information from Apple including reporting scams to Apple see Avoid phishing emails, fake 'virus' alerts, phony support calls, and other scams https://support.apple.com/en-us/HT204759

Identify scams related to purported apple notificationsper Eric Root.

“Apple will always address you by your name or the name they have on file for you, not Dear Customer, Dear Client or by using your e-mail address. The e-mail will be from @apple.com or @iTunes.com. E-mail addresses can be spoofed. You can go to Mail/View/Message/Show all Headers to see more. Apple emails won't have poor grammar/misspellings. Apple e-mails will never contain an attachment. Apple will never request personal information by email such as Social Security numbers, your Mother’s maiden name or full credit card numbers. …

“The only exception to the above I have noticed is if you order something from the Apple Store (apple.com), your receipt will be addressed to Dear Apple Customer. That is a receipt for a purchase you initiated.”

Learn about/Increase security

See If you think your Apple ID has been compromised https://support.apple.com/en-us/HT204145

Increase the Security of your Apple ID https://support.apple.com/en-us/HT201303

iCloud security overview  https://support.apple.com/en-us/HT202303

Ways to keep your information safe on Mac https://support.apple.com/en-gb/guide/mac-help/mh11402/mac

I can't think of any reason they would need all that information. I would just sign out and stop using the account.

Do a name change and a password change on your Apple ID. Note the restrictions in the article.

Apple ID Name Change.        

 What to do after you change your Apple ID or password - Apple Support    I suggest doing this before you change your Apple ID or password.

 Apple ID Password Change.      

 What to do after you change your Apple ID or password - Apple Support     I suggest doing this before you change your Apple ID or password.

If you want more protection, enable 2 Factor Authentication.

Apple ID -Two-factor authentication          

 Two Factor Authentification availability.     

 Apple ID - Using app-specific passwords.     

Apple ID - Two Step Verifications FAQ    

Do they actually have your Apple ID and password? If yes, I'd change my Apple ID and use a different password.

See the instructions below for changing an Apple ID.

Change your Apple ID  https://support.apple.com/en-us/HT202667Read these two sections very carefully to see what is allowed: If your Apple ID is a third-party email address and How to change your Apple ID if it ends with @icloud.com, @me.com, or @mac.com.

Before changing your Apple ID using a computer, sign out of all Apple services that use your Apple ID. If you are going to use an iPhone, iPad, or iPod, then stay signed in with your Apple ID on only that device. This instruction is taken from the above document under the heading Before you change your Apple ID.

For sign out purposes, see Where can I use my Apple ID? https://support.apple.com/en-us/HT202659 “This list is provided for informational purposes only and is subject to change without notice. It's not intended to include every feature or service that uses Apple ID. Visit the Apple ID support page for more information.”

And see What to do after you change your Apple ID or password 

 https://support.apple.com/en-us/HT204071

I don't know anything about Bigo. Does it have a cost? If not, I just not delete it. If you don't delete it, are there any bad consequences.

Exactly.

You are welcome.

Great. You are very welcome. Be safe/