This is covered in the documentation under the section “Static Resources“:
The only allowed way to refer to an image in the bundle is to literally write require(‘image!name-of-the-asset’) in the source.
// GOOD
<Image source={require('image!my-icon')} />
// BAD
var icon = this.props.active ? 'my-icon-active' : 'my-icon-inactive';
<Image source={require('image!' + icon)} />
// GOOD
var icon = this.props.active ? require('image!my-icon-active') : require('image!my-icon-inactive');
<Image source={icon} />
However you also need to remember to add your images to an xcassets bundle in your app in Xcode, though it seems from your comment you’ve done that already.