Warning: Spoilers for Star Wars: The Rise of Skywalker are ahead. MAJOR spoilers.
Rey (Daisy Ridley) got a new name and a new weapon at the end of Star Wars: The Rise of Skywalker, and while the name belongs to a larger legacy, the lightsaber is entirely her own. Rey makes a yellow lightsaber in Rise of Skywalker which expresses her own individuality as a hero and symbolizes the balance she was able to find between the Dark and Light sides of the Force. She's not the next Luke, or the next Anakin. She's just Rey.
Jedi build their own lightsabers, so presumably Rey went and built the yellow one for herself before visiting Tatooine at the end of TROS. The hilt appears to be made of her staff from The Force Awakens and other scavenged parts. It also appears to be double-sided, like the lightsaber Rey wields in her Dark Side vision of herself. The energy source at the center of a lightsaber is called a kyber crystal, and back in the days of the Jedi Order, younglings were sent to the Crystal Caves on the moon on Ilum to mine for their own.
In Rogue One, Jyn Erso wore a kyber crystal on a necklace that was given to her by her mother. We also learned in Rogue One that kyber crystals stolen from the planet Jedha are what powered the Death Star's planet-destroying beam.
A color is assigned to a crystal after it has been assigned to a Jedi. There used to be a meaning to the lightsaber color you chose — kind of like Hogwarts Houses. Blue lightsabers indicated a Jedi who pursued the physical aspects of Force mastery, called Guardians. Green lightsabers were for Consulars, who preferred quiet reflection and research. Yellow lightsabers were for those who sought to balance scholarship and combat, also known as the Sentinels. (All Sith, on the other hand, have red lightsabers, possibly because they use synthetic crystals.)
Eventually, padawans mostly kept to blue and green, sometimes opting for more creative choices like orange, magenta, and Mace Windu's (Samuel L. Jackson) famous purple blade. But the rare yellow lightsaber continues to be associated with the tradition of the Sentinels, who used practical problem-solving and didn't rely on the Force to do everything for them.
It's difficult to say whether or not this played a part in assigning the color yellow to Rey in Rise of Skywalker, as some of this information is no longer canon after Disney acquired Lucasfilm and scrapped large portions of the Expanded Universe. However, the philosophy of the Sentinels is appropriate for Rey, who has seen both the power and the limitations of the Dark Side and the Light Side. She also has abilities outside the Force. Her engineering, piloting, and even some combat skills were acquired when she was a scavenger on Jakku, blissfully unaware of her own Force sensitivity.
Canon aside, the warm tones of the yellow blade hint at the red of Rey's Sith past as Palpatine's granddaughter without burdening her with that darkness. It's a little disappointing that Rey ended up not being "nobody," but while her powers may be genetic, what she chooses to do with them is not. She's creating her own destiny, and a yellow lightsaber is a pretty cool way to start.