One - they never establishd either of them were a Skywalker. Or we would've known by now. You can sit and hope for JJ's mystery boxes to open all you want. That ship has long sailed.
Two - your point would make sense
if she was adopted by the Skywalkers. Which she wasn't. It would also have a tiny bit of validity
if she did something to deserve that surname. Which she didn't. No training from a young age, barely any time spent with Luke and sudden Force powers that come without any build up, just so that the plot can be moved forward. She didn't even have the third lesson given before she left the island and it was just waived at on a deleted scene.Luke didn't start training at a young age either, but guess what - he IS a Skywalker and his father's son. He also spent time
being trained by Yoda and not physically chasing an old hermit through half the film, then having a few mins of "lessons" that barely advance Rey's physical or mental connection with the Force. Leia's training of Rey in TROS has already happened off screen in the beginning of the film - there is no development of the character. And it certainly doesn't make her a Skywalker by any means just that she got to hang around with one for a few months.. off screen.
Three - the Solo name doesn't even remotely have the same weight to it that the Skywalker does in that universe. But when you try to shove the latter's name in a
main saga film title (and these lightsaber shots), while not having the main character even being from that bloodline or having her go through any of the suffering or development that the Skywalkers did - then.. well yeah.
The fact they included this trash line in Solo doesn't do much, as it was in a trash and immediately forgotten film anyway. Which to think about.. is not further away from the truth regarding TROS too