Looks like a macrophylla mophead. They normally develop invisible flower buds between July-August for Spring 2015 so they should be pruned after blooming but before the end of June. Rebloomer varieties will bloom again. The previous owner probably pruned it or was not bothered by it. If it is a bother, wait until it gets dormant and then transplant it elsewhere (where it gets some shade in the afternoon is the safest but your sun is probably not as bad as it is down here in the summer so it may still do fine in full sun). When moving it, water the sun the day before, prepare the new hole ahead of time and move as much of the rootball and roots as you can, including shallow surface level roots. Do not fertilize it when you transplant it; wait until it leafs out and danger of frost has passed.

Honestly it looks like your basic Endless Summer. This is how they behave in the north. They can bloom on new wood so cutting back won't affect that too much.

Regardless of what you do, it probably won't exceed that size in zone 4. Hydrangeas are considered by most to be attractive when overhanging sidewalks by a foot or so.

Also, in zone 4 they'd do best against a house or foundation so moving it away from a house would create worse stem dieback or crown damage over the winter.

Endless Summer is a series not a plant, the one usually referred to as 'Endless Summer' is The Original = 'Bailmer'. There are now several other Endless Summer hydrangeas on the market, probably almost if not entirely all unrelated to one another. See the Bailey nursery web site or the Bailey nursery promotional cards that come attached to the plants for correct naming.

As there are a large number of mophead hydrangea cultivars I wouldn't attempt to name the one asked about here using the photo provided. I will say that it looks like it wants to get a lot bigger than it is now, with that narrow bed not being likely to be large enough for it in future. The time to move it to a better spot would be when it is not in leaf.

Most likely an Endless Summer Original being in MN.

I would move it in the spring before it leafs out (sometime in April) to a spot with afternoon shade. I cut mine back in the spring once I can assess the amount of dieback as it varies year to year. Mulch the crown with leaves.

I agree that they like an eastern exposure in the north (a place with afternoon shade). They can get fairly large when mature, even if not covered. (I cover mine in front and not in back.)

If you want blooms, I'd strongly recommend winter covering. I wouldn't prune back in spring in your zone. They may or may not reflower. This is the first year I'm getting any second flush, and it's just a very few buds that are just now opening.

As far as how to cover, you can search on this site for various suggestions. It's done after the leaves drop. I use masking tape or something like torn strips of sheeting to gather the stems toward the center. Then I put a circle of green plastic "hardware cloth" around that and fill with chopped leaves. I've also heard of using wood shavings - the type that are used for horse bedding.