A device's hostname and a DNS FQDN are not necessarily tied to one another.
Imagine for example that Jane has a server whose hostname is simply "janes-mac-pro"; upon which she runs a web service, an LDAP service, and a mail server. She's been given a single IP address and opens up ports 443, 646, and 587 for clients to connect.
In her case, she has the option to make multiple FQDNs referencing her single IP address. In Bind-style notation it would look like this:
ldap.server.example. 7200 IN A 192.0.2.1
mail.server.example. 7200 IN A 192.0.2.1
www.server.example. 7200 IN A 192.0.2.1
All three FQDNs above point to the same IP address, which in Jane's case is plumbed onto her computer- but none of these is her machine's actual hostname. She could also put in another record referencing that name if she wished.
There are other DNS record types which reference ports and service names, however most people don't need to be familiar with them.
The most common way in which having a different hostname for the device than the "hostname" portion of the FQDN would cause problems is if the device is set up to dynamically update the DNS record using the hostname information. This however is usually manually configured, and not default behavior outside of local Windows networks.