Custom alert dialog in react native?
Both Alert and AlertIOS utilise each platform's native simple alert dialog. On iOS the underlying native component is simplistic and only accepts a title, message, and buttons, with a similar case on Android.
For a more custom approach you could use React Native Modalbox, or React Native Modal - both of which provide a highly-customisable modal component.
In future I'd recommend using JS.coach for a comprehensive list of quality React Native components.