You can't do this right now.
The documentation for Notes on Search Layouts says:
TIP In account search results, you can visually differentiate business accounts from person accounts by adding the Is Person Account field, which displays as the person account icon (Person Account Icon).
You may specify the Is Person Account field as the first column in account search layouts. Otherwise, Account Name must be the first column.
And also in Considerations for Using Person Accounts...
In Lightning Experience and the Salesforce app, person accounts appear in both account and contact search results. In Salesforce Classic, person accounts appear only in account search results.
To help users differentiate person accounts from business accounts in search results, administrators can add the Is Person Account field to the appropriate search layout.
There's also a relevant Idea you could vote on, and probably others as well.
For now, it's probably better to train your Person Account users to use the Contact search instead of Account search, since that more closely aligns with their use case.