How would you go about listing instances using aws cli in certain VPC with the Tag Name, private IP address of instance and instance id?

You need to escape the backslashes in order to format the answer correctly.

aws ec2 describe-instances --query 'Reservations[].Instances[].[PrivateIpAddress,Tags[?Key==`Name`].Value[]]' --output text | sed '$!N;s/\n/ /'

So this is the actual command you want:

$ aws ec2 describe-instances --filters Name=vpc-id,Values=vpc-ac973bc9 --query 'Reservations[].Instances[].[PrivateIpAddress,InstanceId,Tags[?Key==`Name`].Value[]]' --output text | sed '$!N;s/\n/ /'
10.101.255.10   i-91efd39b Server1
10.101.255.9    i-f1e8d4fb Server2

And you don't need .Value[]. You can just use .Value, and that will give the same output.

This is awesome, btw. I will be implementing this myself!

CORRECTION: The above won't work if the value of .Value is "None". This works better:

$ aws ec2 describe-instances --filters Name=vpc-id,Values=vpc-ac973bc9 --query 'Reservations[].Instances[].[PrivateIpAddress,InstanceId,Tags[?Key==`Name`].Value[]]' --output text | sed 's/None$/None\n/' | sed '$!N;s/\n/ /'
10.101.255.10   i-91efd39b Server1
10.101.255.9    i-f1e8d4fb Server2
10.101.255.8    i-f6c2450a      None
10.101.255.7    i-34a6afce Server3

Try this

aws ec2 describe-instances --query 'Reservations[*].Instances[*].[InstanceId,Tags[?Key==`Name`].Value|[0],State.Name,PrivateIpAddress,PublicIpAddress]' --output text | column -t