How do you get the queue name of the active call?

Starting Finesse 11.6(1), you can get the queue number and the queue name from the media properties of the dialog event.

<Dialog>
   <uri>/finesse/api/Dialog/12345678</uri>
   <mediaType>Voice</mediaType>
   <state>ACTIVE</state>
   <fromAddress>2002</fromAddress>
   <toAddress>2000</toAddress>
   <mediaProperties>
      <mediaId>1</mediaId>
      <dialedNumber>2000</dialedNumber>
      <callType>AGENT_INSIDE</callType>
      <DNIS>2000</DNIS>
      <queueNumber>5022</queueNumber>
      <queueName>UCM_PIM.Func.Agents.SG</queueName>	
      <callKeyCallId>217</callKeyCallId>
      <callKeyPrefix>152018</callKeyPrefix>
      <wrapUpReason>Another satisfied customer</wrapUpReason>
      <callvariables>
         <CallVariable>
            <name>callVariable1</name>
            <value>Chuck Smith</value>
         </CallVariable>
         <CallVariable>
            <name>callVariable2</name>
            <value>Cisco Systems, Inc</value>
         </CallVariable>
         <CallVariable>
            <name>callVariable3</name>
            <value>chucksmith@cisco.com</value>
         </CallVariable>
         ...Other Call Variables (up to 10)
         <CallVariable>
            <name>ecc.user</name>
            <value>csmith</value>
         </CallVariable>
         <CallVariable>
            <name>ecc.years[0]</name>
            <value>1985</value>
         </CallVariable>
         <CallVariable>
            <name>ecc.years[1]</name>
            <value>1995</value>
         </CallVariable>
   </mediaProperties>
   <participants>
      <Participant>
         <actions>
            <action>HOLD</action>
            <action>DROP</action>
         </actions>
         <mediaAddress>1081001</mediaAddress>
         <mediaAddressType>AGENT_DEVICE<mediaAddressType>
         <startTime>2014-02-04T15:33:16.653Z</startTime>
         <state>ACTIVE</state>
         <stateCause></stateCause>
         <stateChangeTime>2014-02-04T15:33:26.653Z</stateChangeTime>
      </Participant>
      <Participant>
         <actions>
            <action>RETRIEVE</action>
            <action>DROP</action>
         </actions>
         <mediaAddress>1081002</mediaAddress>
         <mediaAddressType>AGENT_DEVICE<mediaAddressType>
         <startTime>2014-02-04T15:33:16.653Z</startTime>
         <state>HELD</state>
         <stateCause></stateCause>
         <stateChangeTime>2014-02-04T15:33:27.584Z</stateChangeTime>
      </Participant> 
   </participants>     
</Dialog>  

For any version earlier than 11.6(1), Finesse did not have the ability to get the queue number or queue name of the active call.