Yeah, it's a bit weird...

On some forms in the US, it's listed as a suffix. Some agencies enforce it, others do not (SSA does not, for example). And colloquially, when"Senior" dies, the son often stops using "Junior" (though that's not a legal change).

UK, Can, and AUS are similar, but not exactly the same as the US. And NSW in AUS complicates matters by outright prohibiting roman numberals are Jnr/Snr suffixes. Mexico has more restrictions due to the mothers-last-name, fathers-last-name naming convention.

Personally, I dig the Nordic and Arabic "x, son of y, son of z, son of..." patterns.