The reason it changes the display name from FQDN to connect (IPsec) IPv4 is because you might not have anyconnect profile correctly configured for the users.
You can edit the client profile form the ASA and then you would not need to make changes on the hostname filed on client.
For modifying the client profile:-
Go to Configuration> Remote Access VPN > Anyconnect Profile >
Name the profile.
Associate this anyconnect profile with the group policy assigned to the users.
You will be able to see “server list” option.
Just click on Server List, then click on ADD. Fill in the hostname or IP (whichever you wish to connect the users with) of the firewall where you have “Hostname(required)” and “Host Adress” options.
Click on OK and save the configuration.
Once the profile is pushed , AnyConnect users will be able to see the hostname or IP of the firewall and can enter the username and password to connect to the firewall.
Ref: http://www.cisco.com/c/en/us/td/docs/security/vpn_client/anyconnect/anyconnect30/administration/guide/anyconnectadmin30/ac02asaconfig.html#pgfId-1111773
Regards,
Dinesh Moudgil
P.S. Please rate helpful posts.
Cisco Network Security Channel - https://www.youtube.com/c/CiscoNetSec/