Can you whitelist certain words from being auto-corrected?
Generally, you can tap the little × in the autocorrect bubble to block the autocorrect (or pick the left-most choice if using Predictive). Do this enough times and iOS will learn your typing habits and stop trying to correct that word.

For a more permanent solution, you can also add that word into your systemwide custom dictionary.

On iOS, open Settings → Keyboard → Text Replacement → +
Under Phrase enter Morty. Then either leave the Shortcut field blank, or enter morty in lowercase so the name gets capitalized automatically.

Note that these text replacements synchronize across your iOS and macOS devices over iCloud. However if you also want to add a word on macOS, it’s under  → System Preferences → Keyboard → Text.