We can see the customer information on ticket console. But you can not filter tickets by the customer.
There is filter option named Submitter but that searches in Submitter field so it is useless. Tickets created by MyIT Service Requests are created by system user called Remedy Application Service. Thus, Remedy Application Service is written in the Submitter field of Incidents, Changes etc.
There is no option to add ootb customer field (or any other ootb fields) to filtering options.
Currently the only option is to create a custom field, copy customer information to that custom field and add that field to ticket console. Even if you do this, the custom field becomes available in filtering options only if you add that custom field to your preset. So every single user must add this new custom field to their each presets.
Adding Customer to filtering options will be much useful than Submitter.