There's only a workaround I'm afraid, and it's to make the primary field a formula field that combines the info that you want to search by.  In your context, it would be something like

In addition to what Adam mentioned above, the only other workaround to this major problem is to use Fillout’s advanced forms for Airtable.

Fillout lets you update existing Airtable records from a form, and you can search by ANY field that you want.

Hope this helps! If you’d like to hire an expert Airtable consultant to help you with anything Airtable-related, please feel free to contact me through my website: Airtable consultant — ScottWorld 

First time poster….

I’ve created an approach natively within Airtable to be able to search on a non-primary key field, but it requires a bit of setup and a bit of overhead. I needed this approach to be able to update values for an Automation. I’ll try to focus on the key details

• I have table called People where my Primary Key is User Name. I also have a field called User Account. I need to be able to do lookup’s by both fields.
• In the table People, create a sync view with at least User Name and User Account (other fields as needed but not key to the solution).
• Airtable does not let you sync a view to the same base, so I sync’d this view to a 2nd base I own (yeah, this is where the overhead comes in, but I was already using this base for other means and you can create a small simple 2nd base if needed).
• The key to this solution is when you create the sync table in the 2nd base, you make User Account as the Primary Key during sync setup, so now my table is User Account, User Name. (I called the table Reverse People Lookup)
• Now, create a sync’d view from Reverse People Lookup table in the 2nd base back to the original base which will create a new sync’d table (which I also called Reverse People Lookup) and I moved it right next to my original People table. 
• You now can do a lookup on the User Account field in the Reverse People Lookup to find User Name.

Concatenating these 2 fields would have been fine if I was doing a manual lookup but I needed this for an automation so I had to have the exact values.  Yeah, its a bit complex to setup, but what I like is that once I set it up, there is really no further maintenance since the data will always be up to date via the sync’ing nature.

This might not work for everyone, but I want to share the concept out because I felt it could be helpful.