Domain registration failed: [We can't finish registering your domain.

We do not know what type of failure it is, but it would be best to refer to the following official AWS documentation and contact AWS support. [1]

[1] Contacting AWS Support about domain registration issues - Amazon Route 53
https://docs.aws.amazon.com/Route53/latest/DeveloperGuide/domain-contact-support.html
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AWS provides a Basic support plan, free of charge, for all AWS customers. The plan includes assistance for the following issues related to domain registration:
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I followed all steps to register my domain in route53, after that I recieved an email like that:

Dear AWS customer,

We recently received an online request from your AWS account to register the following domain name:

domainname.com

We weren't able to register the domain name. This is because:

We can't finish registering your domain. Contact AWS Support at https://console.aws.amazon.com/support/home?region=us-east-1#/case/create?issueType=customer-service&serviceCode=billing&categoryCode=domain-name-registration-issue for further information. We apologize for the inconvenience. For more information, contact Amazon Web Services Customer Support.

Regards, Amazon Route 53