The sub command ec2 describe-instances doesn’t show whether it has Elastic IPs or not. Another sub command ec2 describe-addresses shows InstanceId and PublicIp.

We can join them with join command representing Name.

$ aws ec2 describe-instances \
	   | jq -r '.Reservations[].Instances[]|[
		       .InstanceId,
		       (select(.Tags!=null).Tags[]|select(.Key=="Name").Value)
		     ]|@tsv' | sort | tee ec2.tsv
i-00d7xxxxxxxxxxxxx     app-01
i-01bdxxxxxxxxxxxxx     db-03
i-04a7xxxxxxxxxxxxx     app-02
i-0636xxxxxxxxxxxxx     db-01
i-0808xxxxxxxxxxxxx     db-02

$ aws ec2 describe-addresses \
  | jq -r '.[][]|[.InstanceId, .PublicIp]|@tsv' \
  | sort | tee ip.tsv
i-01bdxxxxxxxxxxxxx     1x.1x3.xxx.xxx
i-0636xxxxxxxxxxxxx     5x.1x8.xxx.xxx
i-0808xxxxxxxxxxxxx     5x.1x7.xxx.xxx

$ join -a1 ec2.tsv ip.tsv
i-00d7xxxxxxxxxxxxx app-01
i-01bdxxxxxxxxxxxxx db-03 1x.1x3.xxx.xxx
i-04a7xxxxxxxxxxxxx app-02
i-0636xxxxxxxxxxxxx db-01 5x.1x8.xxx.xxx
i-0808xxxxxxxxxxxxx db-02 5x.1x7.xxx.xxx

One-liner works.

join -a1 <(aws ec2 describe-instances \
	   | jq -r '.Reservations[].Instances[]|
                     [
		       .InstanceId,
		       (select(.Tags!=null).Tags[]|select(.Key=="Name").Value)
		     ]
		     |@tsv' | sort) \
	 <(aws ec2 describe-addresses \
	   | jq -r '.[][]|[.InstanceId, .PublicIp]|@tsv' | sort)