The app does not need you to say the full name of the person. For example, if you have only one person in your contacts list named "Jane", you can say "Text Jane", instead of saying "Text Jane Doe".
Another potential fix is to change the speech recognizer that is used. In the Speech Recognition (Advanced) section of the settings, try enabling or disabling Google recognition for commands.
Another option is to say the phone number of the person instead of the name. For example, if Jane Doe's phone number is 202-555-0123 you can say "Text 202 555 0123".