entity_view_mode_delete in core/modules/entity/entity.module

Delete a custom display mode.

entity_view_mode_save in core/modules/entity/entity.module

Save a custom display mode.

field_ui_manage_display_title in core/modules/field_ui/field_ui.admin.inc

Title callback: Gets the display mode name.

field_ui_view_mode_delete_form in core/modules/field_ui/field_ui.admin.inc

Form builder: Delete a display mode.

field_ui_view_mode_form in core/modules/field_ui/field_ui.admin.inc

Form builder: Add or edit a display mode name.

field_ui_view_mode_reset_form in core/modules/field_ui/field_ui.admin.inc

Confirm form: Resets a display mode to using the default display.