A little bit outside of my area; but I believe Azure Traffic Manager is just a DNS load balancing service, returning the nearest IP address of the service to the user.
So if you connect to vpn.company.com, it will return the IP address of the nearest MX. If the MX is configured to use its dynamic DNS name and certificate, it expects a connection to xxx.dynamic-m.com.
However, AnyConnect thinks it is connecting to vpn.company.com, so a certificate issue is created.
If you want to use Azure Traffic Manager then you will need to load a custom certificate onto each MX that matches the original DNS name that AnyConnect is told to connect to. You will also have to manage the process of rolling these certificates each time they get close to expiry. A process prone to failure because humans don't tend to be good at managing this process.
That is why the easier option is to use the AnyConnect Optimal Gateway Selection feature, and have it do everything automatically. You don't have to touch any certificates, nothing. It will keep working year after year without you having to do anything.