I have multiple directly connected servers listed twice in the portal.
When i list "Servers Connected Directly" I see multiple servers that are listed twice. Once with its computer name and once with its FQDN. The reason why the server is also listed with its computer name is one event. All other events are based on its FQDN.
The IIS collection was changed so that it now reports the same (typically, FQDN) computer name also seen in other types of data as opposed to just the NETBIOS name/host name that was inferred from the log content.
This was part of the fix announced here http://blogs.technet.com/b/momteam/archive/2015/05/14/configuration-changes-for-iis-log-collection-in-operations-management-suite.aspx
For actually showing ‘connection’ status of direct agents (not inferred from data in search), vote this http://feedback.azure.com/forums/267889-azure-operational-insights/suggestions/6734080-improve-visibility-of-an-agent-status
Adding some general information for who stumbles here even after the 'known' fix for IIS is out.
Duplicates occur for a few reasons and your environment has examples of 3 different issues:
1) Some data sources report the host name, others the FQDN (e.g. SCOCM vs SCOCM.contoso.com) which results in Op Insights see 2 different computers
2) Some data sources report the name in uppercase, others lowercase (e.g. EXCHANGE.contoso.com vs Exchange.contoso.com)
In my environment SecurityEvent, Event and ConfigurationObject types all have lowercase for a server, while SQLAssessmentRecommendation, ConfigurationChange,RequiredUpdate, ProtectionStatus and UpdateAgent all report an uppercase hostname
3) Some data sources don’t report back the Computer name - i.e. AlertHistory and PerfHourly are both data sources that may not return a computer name
For 1 and 2 you can see which data sources report back what by clicking on the management group name and then clicking on the name of the computer and looking at the list of 'Types' for that machine.