We don't get a lot of generational suffixes in British culture, and as that's the environment amongst which WH40K was written, it's probably not that common in the Imperium either.
As I experience it, "Junior" is far more American than it is British or European. I guess your closest Imperial styled version is the Roman approach: "Secundus", in the same manner as someone might be "Joe Bloggs the Second" .("The Second" is, in of itself, probably also passable).
These are perhaps slightly fancy, but the most traditional uses of generational suffixes in Europe would be as part of monarchy, nobility or (slightly related) the Pope. So it is something I'd think of being used in hive spires, not hive sumps.