The name of your company should in part reflect what it does.
Like, Facebook- you expect to see pics of people.
Now, there are always exceptions, like Apple, Tumblr, Google. You can't tell what they do by their names.
But for a small start up, if you can incorporate what you do into the title, that will give you more hits on a search engine too.
You say it's a "media company" and i'm not sure what that means. So, why not add the word media to your picks so far?
Amenga Media or
To see if the names you have chosen have already been copyrighted by someone else, google the name. When I came up with what I thought was a clever, inventive name for my business, I googled it and 25 hits came up of other people using the same name. So, just make sure.
And good luck to you!