Save the shortcode name in an option, and use that when you add the shortcode:
add_shortcode(
get_option( 'your_plugin_option', 'default_shortcode_name' ),
'your_shortcode_callback'
);
Save the shortcode name in an option, and use that when you add the shortcode:
add_shortcode(
get_option( 'your_plugin_option', 'default_shortcode_name' ),
'your_shortcode_callback'
);