For VoiceOver:
Go to iOS System Settings > General > Accessibility > VoiceOver > Speech > Voices
Select the language which you are using on your device
Select a voice which you prefer
For Speak Screen / Speak Selection:
Go to iOS System Settings > General > Accessibility > Speech > Voices
Select the language which you are using on your device
Select a voice which you prefer
Note: You can only use the voices which your device language is set to. E.g. If your iPad language is set to English (UK), then you can only use voices from that section (e.g. Daniel, Kate) but you can't use voices from English (US) (e.g. Fred, Samantha).
Most voices besides the default ones have to be downloaded.
Unfortunately, the Siri voice is not accessible to 3rd-party app developers. rdar://42656565