The temperature rise of the coil will worsen the working conditions of relay contacts and affect the service life of the contacts, so if it is not necessary, it is best to use rated or lower voltage (generally, it can work normally if it is lower than 75% of the rated voltage).
The main function of the voltage regulator connected to the relay is to protect the circuit, but it will increase the time of contact attraction and release. If you don't have much demand for this time, you can still connect.