Global search uses Quick Find Entity View to search the records. If a field should be searched globally, add the field as a Search column under Quick Find View of the associated entity.
Navigate to Settings > Customizations > Entities > Expand the entity for which the search field should be added. Select on Views and open Quick Find View.
Click on Add Find Columns and select the column that should be searched.
Publish the customization and Search Globally!!
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