You can add an Alias to a non-constituent relationship (and use it as a look up value) if you have a paid data destination that enables you to add relationships (either Individual or Organisation). The screenshot below shows the Individual Relationship tab, but the same functionality is available for Organisation Relationships.
You will also want to add a Criteria Set to the Relationship Criteria sets to enable matching based on the Alias.
For information about how to use this functionality for constituent records, see this knowledgebase article.