What kind of jasmine?

I don't remember the name of the Jasmine but it has little white flowers when it blooms which looks great against the dark green foliage.

Look up Jasminum officinale.

or Trachelospermum jasminoides

Kind of like the jasminoides but the leaves are much thinner. More like the officinale leaves but the blooms are all white and there are not that many flowers as I see in the pictures.

Trachelospermum asiaticum?

Nope, the leaves are about a half inch to three quarters wide.