To change the Records Management URL so that it uses a Fully Qualified Domain Name (FQDN), you must configure Records Management so that it knows the URLs that will be used to access the site. To do so, after configuring DNS, perform the following steps:

Open a PowerShell command window, and execute the following commands:

Set-RecordsManagerWeb -SiteName "Records Management"
-SiteUrl "https://url-to-manageweb"
-WSFedMetaUrl "https://url-to-sts/metadata/federationmetadata.svc/xml"
-WSFedMetaRealm “https://url-to-manageweb”
-WSFedMetaReply “https://url-to-manageweb”
-WSFedMetaAudience “https://url-to-manageweb”
-WSTrustUrl "https://url-to-sts/Trust.svc"
Set-RecordsManagerSTSWeb -SiteName "Records Management STS"
-BaseUrl "https://url-to-sts"
-ExpectedAddress “https://url-to-manageweb"