Use the database Prefix method pops to mind. You could probably do something with the version or build number and incorporate that in the table/collection prefix setting for Hangfire so you don’t even have to change a setting anywhere. This would allow complete segregation of the different versions which you will no doubt want. Specifically since the dashboard would get a little upset with different versions of the assembly containing the jobs.
Or you could use the schema approach (it depends a little as to what Storage DB you are using).
Personally I would suggest something like Mongo, reason being it would require absolutely no setup on the database side to accommodate a new version (with a new Prefix). Collections in Mongo are automatically created if they don’t exist (there is no such thing as a table schema to define which means all you need to create a new collection is a name for it). With something like SqlServer you would have to do additional setup work for each version on the DB side.