@Yakamoz_fs You don't need by or with. You can simply say, "Go off the list" or "Choose from the list" or "Go by the list" (instead of off) or "Pick from the list" etc. There are several ways of saying it. But saying "go off the list" is fine. It's probably not as common as some of the others but it would be understand. Just keep in mind that going off the list could also mean that someone didn't use the list but chose someone else who was not on the list. So in this sense they went "off" the list but in a different way. Hope this makes sense.
@Yakamoz_fs I probably should not have even mentioned this option. Sometimes I give too much information in my answers and I think it can be confusing. Just sort of forget this one and learn about how it means to use a name from the list when you say "off the list", OK?