This is a Japanese Holly (botanical name Ilex crenata), of which there are dozens of cultivars. We can't really make too definitive of a guess as to variety because there's lots of overlap between them and much of the distinguishing traits are based on the mature size and shape of the plant, which will of course be altered when they are pruned. As an educated guess, this specimen might be variety 'Compacta'.

Japanese Holly is often grown as a boxwood-like evergreen, since their spineless leaves look so similar to each other. Like other hollies, they either produce male or female flowers (depending on variety), so male plants never fruit, but female plants (if pollinated by a male Japanese Holly) can produce berries. In the case of Japanese Holly, the berries will be inky-black, not red.

Boxwoods do flower, but their blooms are not very conspicuous (they are yellowish-green and about as small as these holly flowers), and like other shrubs (including holly), if pruned heavily and regularly, they might not bloom much since the flower buds would have been cut off.

Miri