To ensure your messages pass the DMARC check with flying colors, you'll need to make certain the domains listed in the From, Sender, and Mail-From headers match each other exactly. That is, the domain listed in the From header is the exact actual sending domain.

For example, if your sending domain is ABCdomain.com, but your From field shows 123domain.com instead, you will almost certainly run into DMARC issues. Sometimes, even the difference between mail.ABCdomain.com and ABCdomain.com is sufficient for a server to place your message in a spam folder. We make sure that our Email Best Practices are clear that the domain listed in the From header and the actual sending domain should match for exactly this reason.

For better deliverability it is recommended to use the same from domain as the sender,

Domain names do not matter as much if you’re only sending. You can send messages from sales@mycompany.com even if your domain name is called anothercompany.org. Although, it is best for deliverability if you are using the same domain in the From field that the actual sender is using.

Each message you send out has both the sender and from address. The sender domain is what the receiving email server sees when initiating the session. The from address is what your recipients will see. For better deliverability it is recommended to use the same from domain as the sender.

Ultimately, the "On Behalf Of" notation highlights the mismatch between the domain used in the Sender field (mail.example.com) and the domain used in the From field (example.com).  In the above example, the envelope is sent through the domain mail.example.com, but the message is listed as being sent from the domain example.com.

there is no way for Mailgun to prevent an email client from displaying the "On Behalf Of" notation as long as the domains contained in the Sender and From fields don't match.  However, ensuring the exact same domain is used in both fields will eliminate the "On Behalf Of" notation.

Microsoft strongly recommends that you conduct email testing prior to sending live communications to your users/customers

With Mailgun, you'll need to upgrade to a dedicated IP or "managed email service" and pay extra for "better deliverability." At Postmark, great deliverability isn't an up-charge. It's simply included, and we share live delivery data so you can judge for yourself.

Many mail systems allow recipients to report mail as spam or junk, and mail streams from senders whose mail is often reported as junk tend to have poor deliverability. Hence, the mailers want to make it as easy as possible for recipients to unsubscribe; if an unsubscription process is too difficult, the recipient's alternative is to report mail from the sender as junk until the mail no longer appears in the recipient's inbox.