Is there an official site to look up the scientific names of plants?

Also try the U.S. Dept. of Agriculture's http://plants.usda.gov/.

That's probably the best place to start, in general. It mostly just
covers plants which are found in the U.S. (native, introduced, or in
cultivation).

Dave's Garden's plant files at http://davesgarden.com/guides/pf/ are
pretty comprehensive.

Sometimes there will be issues such as the horticulturalists using one
name (often an older one) and the scientists using another.

Even something like whether the cultivated plants are all from the
same species, or from several different species, may require research
(there are a number of species of thyme which are cultivated, for
example).

I wanted to establish the scientific name for the culinary variety
(which I believe might be the "Greek Oregano").

I'm not sure there is just one species which is in culinary use
(varieties, being subdivisions of species, would complicate matters
further). http://en.wikipedia.org/wiki/Oregano mentions at least
three (which are said to have similar flavors). Greek Oregano, at
least according to http://plants.usda.gov/java/profile?symbol=SAFR10
is in the genus Salvia (better known for a number of ornamental
flowers and also Salvia officinalis, the well-known culinary herb).
It isn't clear to me what Greek Oregano tastes like and whether much
of anyone uses it for culinary purposes.

It can be hard to get to the bottom of this kind of thing. For
example, there's the whole "cinnamon" vs "Cassia" issue (with the more
expensive one having the more highly prized flavor, and the
terminology in the marketplace being rather confused/inconsistent,
perhaps because a lot of customers won't know the difference or won't
care).