Where's the record name label stored in the Application Composer?

The Record Name field specifies the display label for the object's RecordName attribute.

You can find this setting within the object definition in Application Composer, where you define or edit custom objects.

You can also use the configuration report from the Metadata Manager for details about the Custom Object including the table and column name where the field details are stored. Here's what you can find in the configuration report.

Report Item	Description
Configuration Summary	Provides a summary of changes such as the number of objects and fields, relationships created, and object validations.
Global functions	Includes a listing of the global functions created.
Relationships	Includes a listing of all the relationships created.
Object summary	Select All changed objects to include all the changes that have been made to any objects. Select Selected objects to include all the changes for only a subset of objects. Tip: To include layout details, select up to five objects only.
Fields	Includes custom fields and standard fields that have been changed for the objects that you selected.
Server scripts	Includes object validations, object functions, object triggers, and global functions for the objects that you selected.
Object workflows	Includes object workflows for the objects that you selected.
Page layout summary	Includes a listing of dynamic page layout names and layout conditions for the objects that you selected. Select Layout details to include a list of all the actions, buttons, subtabs, and field names exposed in each subtab of a dynamic page layout.
Custom object details	Includes details of custom objects and fields that you've created. To view the details of a custom object, simply click its name in the report. You can retrieve details such as the Table Name, which indicates what table the custom object or field belongs to. You can also identify the fields or objects in that table using the Column Name attribute.