Formatting Date field

I have date field which has default format.

I want to change format of that field to MMM-YYYY. How can I do so ?

You have to config the date format like your date string.
Change the string format how would you like and match that in logstash.conf. I think is not possible change the config without change the date string.

is there any way to do it from Kibana ? If yes then can you please write the steps.

For that configuration you have to use logstash. The format date is decided by the string. For example if you have a log that timestamp is like [23/Mar/2017:09:45:15 +0100] you can configure that like
date {
match => [ "timestamp", "dd/MMM/YYYY:HH:mm:ss Z" ]
target => "@timestamp"
}.
So if you want to modify that the first step is modify data passed in ES and config it in Logstash.