Cultivar?

I too would love to know the botanical name of this shrub.

Ilex X 'Conif' (patented hybrid)

As a hybrid, is is correctly named Ilex X 'Oak Leaf Holly' or 'Red Oak Leaf Holly' or Ilex X 'Conif' ;-)

It's a new one in the red holly series. Those are some great looking hollies, and on my list of plants to add to my landscape. I believe that the Red Holly series were derived from seedling selections of Ilex X 'Mary Nell'. I THINK.

As with most hollies, it will stay more compact with plenty of light. If this location gets about 6 hours of direct sun, your plant should respond beautifully.

Its botanical name is a problem, especially since I'm not at the nursery to look at its tag. It seems to be a Red Holly hybrid. I have found it online listed as Ilex x "Oak Leaf", Ilex cornuta "Oak Leaf", and Ilex hybrida "conaf" Oak Leaf. When I saw it at the nursery, seems like it had a generic tag -- definitely not a Monrovia or Iseli product.

Since these red hollies are quite new on the market you may have to become one of those who can report on experiences with it.

here is a photo of mine which has been growing since 2000.(sorry for the poor quality pic)
started with a one-gallon, maybe 18"-24", and it now stands at 8' tall. you can see the form is pyramidal. the site is very bright with some direct sun; there is a mature pine just beyond the shrub that provides shade during mid-day. this view is facing east/southeast. it is not perfectly full of foliage in the center, on the east side, most likely since that is the area that receives less sunlight. i have not pruned it at all. it is standing as a specimen and i also wanted it there for screening the view of the neighbor.
the site linked below say partial shade is preferred by this plant.
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Here is a link that might be useful: red hollies hybrids