Know when a video has ended ?

Yes, with the video selected, just use a trigger with the option "when media completes" and especify the proper media

Something like

Change state of "name" to normal when media completes "name_media"

Just as a pointer, but the trigger dialog box from a programming point of view is backwards !  - for example:

Oh ok

But it works now what you wanted to do?

In addition, you'll want to set the initial state of the button you want to appear after the video is over to Hidden, as in the screenshot below.  A combination of this and Juanjo's media trigger should accomplish what you're trying to do.

http://articulate-tutorials.s3.amazonaws.com/storyline12/Insert/states/initial_state.png

Thats great .. but not so good when you have text inside the square shape, see screendump:

Hummm... i have a button with text inside and that thing works. When you set to initial state hidden, the buttons gets a dark tone, maybe, with your backgruond you can't see that

Same here, I use this technique quite often, and I always have text inside...  Feel free to post a sample .story file if you can't get it to work...