Wow!! Those are gorgeous!! I'm a big fan of shrub dogwoods :-))

Those look to be the variegated red twig dogwood. Generally, rather radical pruning is done on these to encourage new stem growth, which has the most intense bark color.

There's a couple ways of going about this. You can prune back the entire shrub to a height of about 24-30" in late winter. You could leave it a bit higher if you feel that's too severe. Or you can take a third of the stems back to the ground (or as close as you can manage) at the same time of year. You can also trim back the top some if the overall height exceeds what you prefer.

Thank you for the message. I was thinking it was a red twig dogwood, but the pictures I've seen of the dogwood that had been taken care of looked pretty different (actually red :-) ). I think I will try to cut them back in late winter and see how it goes.