Learn English – What would you call x0th anniversary

While several terms loosely fit the criteria (such as a culinarian), a culinophile or reagenteur speaks more to my tastes (if you don't mind portmanteaux).

As for what one might call the group, taxonomy or classification are appropriate when ascribing the term to a family derived from a particular set of criteria. Plenty of additional terms are available in online Thesauri, if you're curious.

Your presumed definition of a 'round number' is only partly correct. Consider this:

1000 is a "rounder" number than 1024.

Also:

1020 is a "rounder" number than 1024.

However,

1000 is a "rounder" number than 1020.

In other words, 1000 and 1020 are both obtained by 'rounding' off 1024. Therefore, a number's 'roundness' is based on two factors: that which it is rounding and the degree to which it is rounding off.

A 'rounded-off' number is the result of an original number being operated upon. The original number cannot be 'defined' (or named) in terms of what it may be rounded into from time to time.

In absolute terms, (see above) one could call such a number a
sharp number

n. A precise or unrounded number.
… Round numbers have a salient conceptual basis (e.g., 10 years are a decade). Sharp numbers do not (e.g., 7 years). Estimates tend to be expressed with round numbers. An experiment is described that examines whether consumers make the false assumption that claims using sharp numbers are less likely to be estimates (i.e., are more factual) than those using round numbers and, if so, whether this makes sharp-number claims more believable. The results demonstrate that such assumptions do occur, particularly for those consumers considered to be advertising skeptics. —Robert M. Schindler, Richard F. Yalch, "It Seems Factual, But Is It? Effects of Using Sharp Versus Round Numbers in Advertising Claims," Association for Consumer Research, October 1, 2005