I was using sandbox domain created by Mailgun. The problem is sent email contains a keyword 'via mailgun.org'.
I know that I can do it by creating a new domain and DNS providers. But I don't have any domain name and I cant use my company domain names for testing that service. So can I create a free domain and DNS provider with no cost and just for testing?
Or suggest any other service providers like Mailgun API but without service provider keywords?
This is not possible. You'll need to own a domain and setup SPF/DKIM records with mailgun (or any other ESP) in order for them to send email "directly" from your domain.
There is no work around, the 'via mailgun.org' exists to flag senders with unauthorized domains.