It looks like a Japanese Yew of some kind. Just planted two of them, but they were a growing upright tree. The greenery is identical and everything about it otherwise. The Hemlock and the Yew look very much alike don't they? The Yew is also very toxic, but so attractive.
The owner of the plant said it was a Yew, but to me, too, it looks more like a Hemlock. It is why I asked. Thanks.
It looks pretty Sundrop. If you decide you want to train it to grow upright, I believe that it would be easy enough to do. I like getting advice from a nursery or google info on a species once I know what it is. All the best.
I don't believe the original poster asked the question re: how to grow it. In any case, a prostrate form of a conifer would have been specifically selected for that genetic characteristic. Training it upright would be an attempt to override its genetic predisposition. If an upright cultivar were to be desired, it would be better to remove this plant and start with something that is predisposed to it.