>>28754999They're just flavor.
What's important, though, is that the level isn't part of the name or anything, it's just flavor text.
With Lv X Pokemon, the "Lv X" is the same flavor text, not part of the name.
Meaning pic related is just "Regigigas", not "Regigigas Lv X", so you could only have four total of normal Regigigas and the Lv X version, not four of each.