I haven't yet found a way to customize the dropdown list in the GUI, but you can use the
Add Sensitivity Classification statement (only in Azure SQL and SQL 2019 so far -- Ugh! Sorry.) to apply any label you want to classify a column.
See this Microsoft documentation for details on the
Add Sensitivity Classification statement. But here are the basics:
ADD SENSITIVITY CLASSIFICATION TO
<object_name> [, ...n ]
WITH ( <sensitivity_label_option> [, ...n ] )
LABEL = string |
LABEL_ID = guidOrString |
INFORMATION_TYPE = string |
INFORMATION_TYPE_ID = guidOrString
Also see this Aaron Bertrand article at MSSQLTips.com.
That being said, even though you have to deal with HIPAA, CJIS, NFIRS, NFPA, and CISSP, and they might not use exactly the same terms as each other, you should still be able to map the sensitivities to the built-in labels. Customizing the labels might work for now, but you'll have to do extra work to maintain that customization, making sure it is consistent across tables, database, and instances, and documenting it well.
I recommend you work with your auditing and compliance folks to reach a mutual understanding of what each sensitivity label means to your organization, and how to map that to the various regulatory expectations.