I was given a small but beautiful hydrangea and it has bloomed for the last 2 years. (It even bloomed right after I planted it last spring)
I have several varieties, but haven't seen one like this. It's a type of lace cap, but the bloom itself is as big as a dinner plate or larger!! It's my favorite, but would love to know it's name...

Is it the one called "Shooting Star"?

Maybe Lacecap Hydrangea (Hydrangea macrophylla 'Hanabi')

It seems that the hydrangea may be both 'Shooting Star' and 'Hanabi', if the information about the name at this link (scroll down to the bottom) is correct. There are certainly plenty of other examples of plant names getting translated or renamed, but it sounds as though the breeder named the hydrangea 'Sumida-no-hanabi'.
http://rainyside.com/plant_gal...
It's a lovely flower; I hadn't seen that one before, but I really like it.

Virginia

Yes, all three of those names are included in the entry that I posted.

Hanabi is Japanese for 'fireworks'. Sumida is a river that runs through Tokyo. Sumida no Hanabi would loosely translate to 'Sumida River of Fireworks' which happens the last weekend in July.

I agree, it looks like Lacecap Hydrangea (Hydrangea macrophylla 'Hanabi') which, as shown in our database (above link) is also sold as:

Shooting Star
Sumida-no-Hanabi