Take a copy of this picture to a true plant nursery (not a big box store). They should be able to help you. Good luck.
That looks like Montauck Daisy. These are the ones I have,
Hi Mariposa, When does this daisy bloom?
looks just like my montauk daisy too.
Jan...they should be showing some type of buds soon for you. Enjoy!
am anxious to see if it has a bloom. The leaf looks like a Daphne.
Jan, Montauk daisy as Mariposa said. They are in bud right now, Early fall bloom up north. Hi Beverly from Smithtown. I'm a L.I gal too, moved up north 30 yrs ago.
it is Montauk daisy and yes it is a fall blooming daisy in the south up north it is late summer
I have a few Montauk daisies in my garden and last year they were pretty big and floppy when they finally bloomed in the fall so this year I cut them back by a third in mid June. They looked pretty ragged until recently, now they are filling in and beginning to make buds. Last summer they were still blooming when the Muhly grass turned pink in October (zone 7a). They are a nice plant if you have the space!
I don't know the generic name of this but it's called a daisy bush. A neighbor gave me a cutting a couple of years ago. Now it's threatening to take over my space.. If it isn't cut back a few weeks after all the pretty white flowers are gone it will spread to twice the size by next spring. Flowers in late July thru August here in Massachusetts.
I always cut mines down in early Spring it makes for a more compact more attractive display.
Here is a link: