My refund was approved but Chimes couldn't accept my deposit cause my name wasn't on the card which will be in the account by Feb 21st, will they mail it out instead???

Yes. The IRS will mail your refund check to the address on your tax return.

https://ttlc.intuit.com/replies/3302459

Can Chime put it into another Chime account that has my name on it? 

You would have to call Chime to check and see if they still have the refund amount. If Chime could not accept your refund, it is a possibility that it got sent back and then the IRS will just mail you out a check for your refund. You can also call the IRS directly to check on the status of your refund.