It's a type of bigleaf hydrangea, Hydrangea macrophylla. It looks bit rough - but not too bad. It would prefer to have some afternoon shade and a more organic mulch than the rocks.

Most of the flowers have just gone past their prime and that could be an indication that a bit more watering would have been appreciated as well.

It was neglected while the house was for sale and I hear you about the mulch. Previous owners put down rock with landscaping fabric underneath and I don‘t even know where to start with that. Should I cut off the sad blooms?

Sure, you can snip off any flowers that bother you back to the next leaf node.

"Previous owners put down rock with landscaping fabric underneath and I don‘t even know where to start with that."

I hear ya :-)) It's a lot of work but remove it when you can. Neither is doing any plants in your garden any favors. And it doesn't keep weeds away any better than any other mulch and is harder to keep clean and weed free.