Is there a way to check the other web sites that are on the same server as my?
I have a couple of sites that are just consistently slower than the rest and I’d like to see who I’m sharing space with.

Yes,whois.sc offers a service that show sites being hosted (as well as parked domains) on the same server.

I think the best way you could actually get that to happen is if you contact yout host and see if they are allowed to tell you.

you can request your web host to change your server because you are paying for it