See the Terraform Route53 Record docs

You can add a basic CNAME entry with the following:

resource "aws_route53_record" "cname_route53_record" {
  zone_id = aws_route53_zone.primary.zone_id # Replace with your zone ID
  name    = "www.example.com" # Replace with your subdomain, Note: not valid with "apex" domains, e.g. example.com
  type    = "CNAME"
  ttl     = "60"
  records = [aws_lb.MYALB.dns_name]
}

Or if you're are using an "apex" domain (e.g. example.com) consider using an Alias (AWS Alias Docs):

resource "aws_route53_record" "alias_route53_record" {
  zone_id = aws_route53_zone.primary.zone_id # Replace with your zone ID
  name    = "example.com" # Replace with your name/domain/subdomain
  type    = "A"

  alias {
    name                   = aws_lb.MYALB.dns_name
    zone_id                = aws_lb.MYALB.zone_id
    evaluate_target_health = true
  }
}

Yes, it is possible to create CNAME to the public DNS name ${aws_lb.MYALB.dns_name} or aws_lb.MYALB.dns_name with aws_route53_record resource if you use the domain with a subdomain but not apex domain(naked domain, root domain).

So the code below in Terraform(v0.15.0) works properly for CNAME with the domain which has a subdomain. *CNAME with apex domain(naked domain, root domain) causes error.

resource "aws_route53_zone" "myZone" {
  name = "example.com"
}

resource "aws_route53_record" "myRecord" {
  zone_id = aws_route53_zone.myZone.zone_id
  name    = "www.example.com"
  type    = "CNAME"
  ttl     = 60
  records = [aws_lb.MYALB.dns_name]
}

In addition, the code below in Terraform(v0.15.0) works properly for A or AAAA with apex domain(naked domain, root domain) even for the domain with a subdomain.

resource "aws_route53_zone" "myZone" {
  name = "example.com"
}

resource "aws_route53_record" "myRecord" {
  zone_id = aws_route53_zone.myZone.zone_id
  name    = "example.com" # OR "www.example.com"
  type    = "A" # OR "AAAA"

  alias {
      name                   = aws_lb.MYALB.dns_name
      zone_id                = aws_lb.MYALB.zone_id
      evaluate_target_health = true
  }
}