In Exchange 2003 and Exchange 2007 when clients would attempt to connect to a mailbox it would be based on the server where that mailbox was homed. Specifically these attributes would contain information about the server where a particular mailbox was homed:
In Exchange 2010 a mailbox object is no longer associated with a server but rather is associated with a database. A database has copies which are associated with a particular server. When a client or application attempts to access the mailbox, the active manager process is responsible for locating the server that hosts the active copy of the database and referring mailbox requests to that server. Although not utilized, the Exchange 2010 mailbox provisioning process still stamps HomeMTA and msExchHomeServerName. In this case the attributes are stamped based on the server where the database copy was active at the time the mailbox was provisioned.
Management commandlets like get-mailbox will return the server name stamped in msExchHomeServer. In many cases this is a valid server within the environment. In some instances, the server mentioned has been decommissioned and is no longer available. Although this server name is displayed this is not an issue. There should be no reason that administrators need to update these values as they are not utilized in Exchange 2010.
[PS] C:\Windows\system32>Get-Mailbox Tim
Name Alias ServerName ProhibitSendQuota
---- ----- ---------- -----------------
Timothy J. McMichael Tim dag-4 unlimited
homeMTA: CN=Microsoft MTA,CN=DAG-4,CN=Servers,CN=Exchange Administrative Group (FYDIBOHF23SPDLT),CN=Administrative Groups,CN=Organization,CN=Microsoft Exchange,CN=Services,CN=Configuration,DC=domain,DC=com;
msExchHomeServerName: /o=Organization/ou=Exchange Administrative Group (FYDIBOHF23SPDLT)/cn=Configuration/cn=Servers/cn=DAG-4;
Updated second paragraph where I referenced homeMDB instead of homeMTA.