When I copy and paste a figure from Matlab, why don't I get the figure's name?

When I plot data, the figure containing the plot has a name. Each plot in the figure has a title. When I go to the figure's edit menu, and select "copy", and then paste the figure into a Word document, I get the plot, with its title, but not the figure's name. Is there a way I can get the figure's name as well?

Here's the way the figure looks when created in Matlab:

And when it is copied and pasted into another document, it looks like this:

I don't want it to copy the menus and buttons, but I would like the title, "Random Data" to be copied and pasted.