Check an IP address has a reverse name, and that the name resolves back to it.
A reverse DNS record maps an IP address back to a name. For web servers nobody cares. For mail servers it is close to mandatory: many large receivers reject or heavily penalise mail from an address with no PTR, and it is one of the first things they check, before they look at your content at all.
The part people miss is that a PTR on its own is not enough. Receivers check the round trip: the address reverses to a name, and that name must resolve forward to the same address. That is called forward-confirmed reverse DNS, and it exists because a reverse name alone can be claimed by anyone who controls the address block.
This is also the one record you often cannot set yourself. Reverse DNS is delegated with the address block, so it is your hosting provider or network operator who publishes it, usually from a field in a control panel next to the IP.
Whoever controls the IP block, which is normally your host. On most providers it is a single field beside the address in the control panel; on others it is a support request.
A real hostname you control that resolves back to the same address, ideally the name your mail server announces in its HELO. Matching all three is what a strict receiver is looking for.