There is an app called Picture This. I have it on my IPad and used it a couple of times. Just take a photo of the plant and hey presto! Think it is free the first few times then it has to be paid for. I am sure there are other plant identification apps to be had.
I think Gransooz is right, a hebe. Cuttings of hebe take very easily. It off some sprigs about 3 inches long (preferably without flowers but pinch flowers off otherwise). Remove the leaves on the bottom half of the sprigs. Push the cuttings into a pot of gritty compost, water well and place out of direct sun.
It looks like a hebe but I don’t know enough about them to tell which one. Maybe this helps a bit and you could check online looking through the different ones. Sorry I couldn’t be more helpful.