It is possible that the bright shining star you saw next to the Moon last night was actually not a star, but a planet. The position of planets in the night sky changes over time, so it is important to know the date and time of the observation to determine which planet it might have been.
Assuming it was a planet, the two most likely candidates are Venus and Jupiter. Venus is often called the "evening star" or the "morning star" because it is one of the brightest objects in the sky and can be seen just after sunset or just before sunrise. Jupiter is also a very bright planet and is currently visible in the night sky in many parts of the world.
If you can provide more specific details about the time and location of your observation, it may be possible to determine with greater certainty which celestial object you saw next to the Moon.