If you want to purchase new, you have exactly four choices of 70-200mm f/2.8 for use on a D500.
https://www.bhphotovideo.com/c/compare/Nikon_AF-S_NIKKOR_70-200mm_f_2.8E_FL_ED_VR_Lens_vs_Nikon_AF-S_NIKKOR_70-200mm_f_2.8G_ED_VR_II_Lens_vs_Sigma_70-200mm_f_2.8_DG_OS_HSM_Sports_Lens_for_Nikon_F_vs_Tamron_SP_70-200mm_f_2.8_Di_VC_USD_G2_Lens_for_Nikon_F/BHitems/1292140-REG_644741-GREY_1436298-REG_1317272-REGI would recommend you do a deep dive of research on each of those, to help you decide. You will have a hard time finding someone who has used them all.
I have little doubt that all four of those lenses are quite capable. The differences in image quality are probably rather minimal.
It may be other factors that set one lens or another apart. For example...
- Look closely at autofocus performance. Basketball is quite fast action and you need a lens that can keep up... acquiring focus instantly and tracking well. The D500 has an excellent AF system, so the lens... along with your setup, skill and technique... will decide whether you get a good percentage of focused images or not.
- Weight can be a consideration. The Sigma (like most Sigma) is a bit larger and about a half lb. heavier than the other three lenses. That doesn't sound like much, but can become a factor toward the end of a two hour game!
- One way to deal with weight is to use a tripod... of, possibly better, a monopod. If you use the common Arca-Swiss compatible quick release mounting system, both the Sigma and the Tamron have a dovetail built right into their tripod mounting rings. No need to buy and fit those lenses with lens plates. I don't believe this is the case with either of the Nikkors.
- Another way to reduce weight a little for handheld use might be a removable tripod mounting ring. Check to see what's possible with each of these lenses.
- When it comes to image quality, look for chromatic aberration at longer focal lengths. It's not uncommon in telephotos. While it often can be corrected in post-processing, there still may be some slight softening or loss of detail. It would be best if there was minimal CA to begin with and I suspect the Nikkor FL (fluorite) lens is the best of the four at suppressing CA.
Out of curiosity I looked at the image quality comparisons of these four lenses at The-Digital-Picture.com. Unfortunately there is no way to do a head to head comparison of the Tamron and Sigma versus the two Nikkors. The test shots there done with the Sigma and Tamron were done on a 50MP Canon 5DS-R. The test shots from both Nikkors were done using a 36MP D810. Usually the higher a camera's resolution, the more punishing it is of lens quality. Trying to take the difference in the cameras into consideration, I would rank the Nikkor 70-200mm FL as the best of the bunch. What surprised me was how close the Tamron G2 comes to it. The Sigma isn't far behind either. Especially at the 200mm end, the "weakest" of the bunch is the Nikkor 70-200mm "II". But even that lens is quite good and stopping it down just a little sharpens it up quite nicely. At 200mm it just isn't quite as good wide open as the other three. This ranking of the Nikkor FL #1, Tamron G2 #2, Sigma Sport #3 and Nikkor II #4 is also supported by a comparison of the lenses' respective MTF charts.
To put all this in perspective, at its 70mm setting all four of these lenses are sharper than the older Canon 70-200mm f/2.8 that I use. It matches the Tamron or the Sigma pretty well at 200mm. I still happily use that lens and have no plans to "upgrade" although there are two newer versions from Canon. Yeah, they're a wee bit sharper, but the main improvement I see is better image stabilization. Just not enough to make me get out my credit card!