So it should read:
UPDATE iweb_conf_demo
SET iweb_conf_demo.Attendee_ribbons = '0770'
WHERE Name.ID, Name.FULL_NAME, Name.MEMBER_TYPE, Name.CATEGORY, Name_Demo.Training_Date
FROM (iMIS.dbo.ISGWEB_CONF_MTR_AGMT ISGWEB_CONF_MTR_AGMT INNER JOIN iMIS.dbo.Name Name ON ISGWEB_CONF_MTR_AGMT.ID=Name.ID)
INNER JOIN iMIS.dbo.Name_Demo Name_Demo ON ISGWEB_CONF_MTR_AGMT.ID=Name_Demo.ID
WHERE Name.MEMBER_TYPE='RES' AND (Name.CATEGORY='CAPF' OR...