Hi Victoria, and welcome. It will be much easier for us to ID that bush once it blooms. There are a lot of things it could be. Looks like it was purposely planted and also has had some shaping so probably not a weed.
Also, hate to say it but this is probably not the time to be thinking about moving that big a plant. Unless you have a back hoe, you'll never get a big enough root ball with it to let it survive a move. The plant is growing well in full sun, there so you will need to find another spot in full sun. The sun right now is 3 weeks away from the strongest it can be, so the plant will be terribly stressed and most likely die if you move it now. Wait until late September at the earliest.
If it were mine, I would thin out some of the older stems, right at the base, so that it will have a nicer more graceful shape, and wait until the fall to decide if you like it well enough to move it.
But please do post more pictures of it when it is in bloom?
