The variable name (such as accelerometerCharacteristic_X) is internal to your ArduinoBLE code:
BLEShortCharacteristic accelerometerCharacteristic_X( BLE_UUID_ACCELEROMETER_X, BLERead | BLENotify );
The UUID (BLE_UUID_ACCELEROMETER_X) however is exchanged with the central device once it has connected to the peripheral device.
To make this characteristic meaningful to any central device you create Descriptors (there are a number of different options available). This information is exchanged upon a read request.