First make sure that you have an end user attached under computer asset info.

To check go to  Computer-> Inventory. Scroll to the bottom and click asset then click Edit this asset. You should see somethign like the following.  

If you have this then the following rule will auto attach this computer when a ticket is opened by this user.

 

SETTING* Frequency: On Save

*********************SELECT QUERY********************************

select HD_TICKET.*,
HD_STATUS.NAME AS STATUS_NAME,
HD_STATUS.ORDINAL as STATUS_ORDINAL,
HD_IMPACT.ORDINAL as IMPACT_ORDINAL,
HD_CATEGORY.ORDINAL as CATEGORY_ORDINAL,
HD_PRIORITY.ORDINAL as PRIORITY_NUMBER,
HD_TICKET.ID as TICKET_ID,
STATE,
if((datediff(DUE_DATE, now()) = 0), 2, if((datediff(DUE_DATE, now())<0), 1, 3)) as SORT_OVERDUE_STATUS,
if(unix_timestamp(TIME_OPENED) > 0, TIME_OPENED, 1<<62) as SORT_TIME_OPENED,
if(unix_timestamp(TIME_STALLED) > 0, TIME_STALLED, 1<<62) as SORT_TIME_STALLED,
if(unix_timestamp(TIME_CLOSED) > 0, TIME_CLOSED, 1<<62) as SORT_TIME_CLOSED,
if(unix_timestamp(ESCALATED) > 0, ESCALATED, 1<<62) as SORT_ESCALATED,
if(unix_timestamp(HD_TICKET.CREATED) > 0, HD_TICKET.CREATED, 1<<62) as SORT_TIME_CREATED,
if(unix_timestamp(HD_TICKET.MODIFIED) > 0, HD_TICKET.MODIFIED, 1<<62) as SORT_MODIFIED,
if(unix_timestamp(HD_TICKET.DUE_DATE) > 0, HD_TICKET.DUE_DATE, 1<<62) as SORT_DUE_DATE,
case upper(STATE)
when 'CLOSED' then unix_timestamp(HD_TICKET.TIME_CLOSED) - unix_timestamp(HD_TICKET.TIME_OPENED)
when 'OPENED' then unix_timestamp(NOW()) - unix_timestamp(HD_TICKET.TIME_OPENED)
else unix_timestamp(NOW()) - unix_timestamp(HD_TICKET.CREATED) end as AGE,
if ((LENGTH(U1.FULL_NAME) = 0), U1.USER_NAME, U1.FULL_NAME) as OWNER_NAME,
U1.FULL_NAME as OWNER_FULLNAME,
U1.EMAIL as OWNER_EMAIL,
if (U1.ID is null, 'z', concat('a', if ((LENGTH(U1.FULL_NAME) = 0), U1.USER_NAME, U1.FULL_NAME))) as SORT_OWNER_NAME,
if ((LENGTH(U2.FULL_NAME) = 0), U2.USER_NAME, U2.FULL_NAME) as SUBMITTER_NAME,
U2.FULL_NAME as SUBMITTER_FULLNAME,
U2.EMAIL as SUBMITTER_EMAIL,
if (U2.ID is null, 'z', concat('a', if ((LENGTH(U2.FULL_NAME) = 0), U2.USER_NAME, U2.FULL_NAME))) as SORT_SUBMITTER_NAME,
if (U3.ID is null, 'z', concat('a', if ((LENGTH(U3.FULL_NAME) = 0), U3.USER_NAME, U3.FULL_NAME))) as SORT_APPROVER_NAME,
if(APPROVAL='rejected', 'Rejected', if(APPROVAL='info', 'More Info Needed', if(APPROVAL='approved', 'Approved',
if(APPROVER_ID>0, 'Pending', '')))) as APPROVAL_STATUS,
Q.NAME as QUEUE_NAME
from (HD_TICKET, HD_PRIORITY, HD_STATUS, HD_IMPACT, HD_CATEGORY)
LEFT JOIN USER U1 on U1.ID = HD_TICKET.OWNER_ID
LEFT JOIN USER U2 on U2.ID = HD_TICKET.SUBMITTER_ID
LEFT JOIN USER U3 on U3.ID = HD_TICKET.APPROVER_ID
LEFT JOIN HD_QUEUE Q on Q.ID = HD_TICKET.HD_QUEUE_ID
LEFT JOIN MACHINE M1 on M1.ID = HD_TICKET.MACHINE_ID
where HD_PRIORITY.ID = HD_PRIORITY_ID
and HD_STATUS.ID = HD_STATUS_ID
and HD_IMPACT.ID = HD_IMPACT_ID
and HD_CATEGORY.ID = HD_CATEGORY_ID
and (( (1 in (select 1 from MACHINE where HD_TICKET.MACHINE_ID = 0)) ) and HD_TICKET.HD_QUEUE_ID = 1 )

**************************END SELECT***************************************

SETTING* Run an update query, using the results from the one above

*******************UPDATE QUERY********************************************
UPDATE
HD_TICKET Inner Join
USER On HD_TICKET.SUBMITTER_ID = USER.ID Inner Join
MACHINE On USER.USER_NAME = MACHINE.USER SET HD_TICKET.MACHINE_ID = MACHINE.ID WHERE HD_TICKET.ID IN (<TICKET_IDS>)

*************************END UPDATE****************************************