With newer UCC SSL certificates it is often not possible to register local domain names.  Example:  mail.mydoman.local
Using the default exchange 2013 setting the outlook 201 client will get a “Security Alert” the says “The name on the security certificate is invalid or does not match the name of the site”

I resolved this by changing the Auto Discover Service Internal Uri.

First I stated the exchange Server 2013 power shell.
And ran these commands:

Get-ClientAccessServer
Get-ClientAccessServer -Identity ExchangeServerName | fl  *
Set-ClientAccessServer -Identity VR-EXCHANGE -AutoDiscoverServiceInternalUri: https://ExchangeServerName.domain.com/Autodiscover/Autodiscover.xml
Get-ClientAccessServer -Identity ExchangeServerName | fl  *