Having a dynamic IP creates a few challenges as you need some way of keeping the IP up to date.
The company you have registered the domain with will have DNS servers for you to use (nameservers), but rarely do they have a dynamic DNS client you can use to update the IP with those nameservers. Even if they do it can take up to 24 hours to propagate the updated IP, by which time it is already out of date.
Ideally get a static IP, however that's not always an option. Another way will require using a dynamic DNS company such as DnyDNS. I know they are no longer free but others such as NoIP are. The advantage with a paid subscription is increased pool of domain names and no risk of dropping domains due to non use.
Anyway whichever you choose, set up a domain name or two with chosen dynamic dns company,
using the dynamic update client in your synology box set it up to update those domains with the correct IP and check that it works. Once you are sure that it does then go to your domain registrar and set up the mail DNS. MX DNS require hostnames, IP addresses are not allowed.
Setup the MX DNS to point to your dynamic DNS hostnames,
The numerical value relates to the order it should try the hostnames, the lowest number being first.
Now when a mail is sent to you 'email@example.com
' it will look for mx records for 'mydomain.example.com'. It will find them pointing to 'mxmail.mydomain.example.com' and try to send them to the IP associated with that domain. If it is up to date using the dynamic DNS updater then it will reach your Synology.
As an additional measure, consider using Rollernet.us
They offer a free backup MX service as long as your traffic is very small, it would only deal with mail if it failed to reach your mailserver, for example if your IP was slightly out of date, and then send it on once it had been updated. Instructions on how to use them are on their website and you would add it to your MX records as the lowest priority.
That kind of setup should enable a reliable working mailserver on a dynamic IP.