In your DigitalOcean Control Panel, make sure that the hostname you've assigned to your droplet is a fully qualified domain name (FQDN).

Yes FQDN she FQDN... Only messages from mailboxes do not reach the required destination.

Have you rebooted your droplet? Also, make sure you have an A record in the DigitalOcean DNS Manager, pointing to your droplet.

Yes, I rebooted the droplet.
A record in the DigitalOcean DNS Manager has the following form: @ 146.185.172.51.
Even now, I tried to send an email, but the email does not reach the addressee. Instead, after 5-6 hours I get a letter from MAILER-DAEMON@control.yourdomain.com (Mail Delivery System) with the title: "Delayed Mail (still being retried) "
and the text:
"Your message could not be delivered for more than 4 hour(s).
It will be retried until it is 5 day(s) old.

For further assistance, please send mail to the postmaster.

If you do so, please include this problem report. You can
delete your own text from the attached returned message.

The mail system

: host mx1.fullspace.ru[81.222.134.105] said: 550
X-Host Lookup Failed: Reverse DNS lookup failed for 146.185.172.51 (failed)
(in reply to RCPT to command)

: host mx1.fullspace.ru[81.222.134.105] said: 550
X-Host Lookup Failed: Reverse DNS lookup failed for 146.185.172.51 (failed)
(in reply to RCPT to command)

Reporting-MTA: dns; control.yourdomain.com
X-Postfix-Queue-ID: 04F76120F00
X-Postfix-Sender: rfc822; dir@yutrust.ru
Arrival-Date: Sat, 16 Nov 2013 17:33:07 +0000 (UTC)

Final-Recipient: rfc822; admin@r*******.ru
Original-Recipient: rfc822;admin@r******.ru
Action: delayed
Status: 4.0.0
Remote-MTA: dns; mx1.fullspace.ru
Diagnostic-Code: smtp; 550 X-Host Lookup Failed: Reverse DNS lookup failed for
146.185.172.51 (failed)
Will-Retry-Until: Thu, 21 Nov 2013 17:33:07 +0000 (UTC) "

What should I do?

A couple of things;

1. Make sure to change 'control.yourdomain.com' in the Postfix config file. You want to set the domain and hostname in the config file to match your mx records.

2. The rDNS (PTR) records should match your mx records for the server your mail server is on. So if you have 'site1.com' and your mx record is 'mail.site1.com' then you'll want to rename the hostname for your droplet 'mail.site1.com'. If, however, you have 2 droplets and one of those droplets is a dedicated mail server then only that droplet needs to have a hostname of 'mail.site1.com' while the other can be whatever you need.

3. AFAIK DO only allows 1 rDNS (PTR) record per droplet/IP. If you want 3 rDNS (PTR) records, as in your example, you have to create 3 droplets.

I would love the ability on DO to have multiple PTR records for a single IP or multiple IPs per droplet. Here's to looking towards the future.

Thanks to everyone for participating. Worked a day after renaming in control panel DO droplet on FQDN

3. AFAIK DO only allows 1 rDNS (PTR) record per droplet/IP. If you want 3 rDNS (PTR) records, as in your example, you have to create 3 droplets.

That how it is for every provider. A single IP address cannot have more than one PTR/reverse DNS record.

Kamal, not correct for your last statement. you can have as many PTR records for an IP as your heart desires. It is functionally and technically correct.