By default, the SMTP banner showed by Exim is the hostname of your server. You can view it easily connecting to your mail server:
$ telnet mail.yourdomain.tld 25
Trying 203.0.113.1...
Connected to mail.yourdomain.tld.
Escape character is '^]'.
220 here.you-will-see-the.hostname <-- this is the hostname you must use for the reverse dns
Edit: if you don’t have telnet installed and don’t want to install it, you can also use openssl:
$ openssl s_client -connect mail.yourdomain.tld:465 -quiet 2>/dev/null
220 here.you-will-see-the.hostname <-- this is the hostname you must use for the reverse dns
If you use the hostname Exim is showing, you won’t have any problem.