First of all, you should never directly alter the default themes. You should make all your changes in a child theme. Making a child theme is trivially easy and takes about 10 minutes.
Having said that, you have a couple of ways of removing your page titles. Firstly, if you define a custom menu to act as your primary navigation menu (which you will almost certainly want to do at some stage anyway) you can assign the label that you want to appear in the menu to the "Navigation Label", in the Dashboard Menu editor. Then you can remove the title from your page altogether, so that it doesn't have a title and won't appear anywhere. I'm pretty sure that'll work, but you'd have to be careful when creating new pages and check the permalinks, especially if you create pages without titles in which case the permalink may not be what you want and you might have to edit it. I'm not sure how a page created without a title would show up in the Menu Editor either and don't have time to experiment at the moment. WP just allocates a number to pages without titles: but this may also depend on your permalink settings.
The other way would be to give your page a title, but simply not display it in the situations where you don't want it. This will probably mean removing the following code:
<h1 class="entry-title"><?php the_title(); ?></h1>
</header><!-- .entry-header -->
from, at least, the content-page.php file in your child theme's directory.
If you wanted to remove the title in other types of page you might also have to look at removing the equivalent code from some or all of the content*.php pages. There are eleven of these in total, in the twentyeleven theme.
Or you could alter your child theme's CSS to set
display:none; for the headings.