It is a hydrangea macrophylla. I would try adding some phosphorus to see if it helps with the purple color. They need to be introduced into sunlight gradually or the leaves in direct contact with the sun will turn yellowish all around (but the inside leaves will remain green). Hydrangea macrophylla comes in two flavors based on the type of blooms that you get. The one that you have is called a mophead bloom. They also have another type called lacecap, where the bloom has one or two rows of sepals growing around the rim of a center mass of very small flowers. They grow anywhere from 3-6' high. The ones you normally get from a florist or grocery store are only hardy to zones like Zone 7-ish. While you could grow them in containers too, you would need to protect them in a heated garage as your winters will be way too cold for H macrophylla. However, there are other varieties called paniculata (has panicle-type blooms) and arborescens (also has mophead and lacecaps-types of blooms) which are hardy to your zone. They all like well draining, acidic, moist (not wet!!!) soil. Water them when the soil feels almost dry to the touch. This way, the roots will not be in wet conditions and get root rot. All varieties are normally deciduous during the winter months. The blooms will change color as they age and they remain on the plant thru the Winter months. Macrophyllas produce new flower buds around July-August and most paniculatas will produce flower buds in the Spring instead.

If you want the specific name of the plant, you'll probably just want to compare with other mopheads on sites like the "Plant Finder" or look for further clues. The very bottom of the wrapper or pot may have the name of the grower on it. Try contacting them and asking.

Otherwise, look in the top part of the soil - often a tag is stuck in there ID'ing the variety.

My guess is you've got something like a Merritt's Supreme, which are the most common pink "gift" hydrangeas, as they are able to be forced to bloom from a young age very quickly! Some other pinkish ones could be Mathilda Gutges or Firelight.

Once again, just about all gift hydrangeas are macrophyllas.