Watch politicians. The good ones never lie. They make vague statements that were true once, but may not be now and speak in the past tense, they avoid answering the question, they put qualifiers around everything.
1. "I have been called X" works. Making a truthful statement about the past is always acceptable. Of course its really douchy to look at a follower and say "Call me Ceaser". He does. Then tell the players "I have been called Ceaser". If you can't answer then say something like "My name isn't important", "I have many names", "You may call me what you wish", "We are in a Church so lets go with Mr. Church". There are so many variations there is no reason for this to be a problem.
2. Is your truthsayer an oracle? They shouldn't be answering questions about the future directly unless they know the future because if they make any statement about the future that doesn't come to pass they lied. Their answer should be something like "death is always an option", "it is possible you could survive", "it would be safe for me". Your truthsayer simply can't say that the action will or won't kill the person unless they have knowledge of the future. They can suspect and be pretty sure it will, but something in the universe could make it so that they would be wrong and hence lie.
3. Gramatically the person is lying. Without additional qualifiers when saying the "sky is red" it applies to the present location and time, not some unstated far off place or time. You cant say "the sky in red" and then think in your head "on Venus" and make it count. The person spoke a lie, they spoke and thought the truth.
4. If you directly pulled this crap as described after I punched you in the face I'd leave and never game with you again. You can speak in code, but you must first notify the listeners you are doing so, and they need a copy of the code or a basis to translate it. They don't have to have read it just had it made available. Now if they miss the line or misunderstand "Admiral, if we go "by the book". like Lieutenant Saavik, hours could seem like days. " that's their fault. But they were told you were speaking in code, and what the code was. Spock is a great example, he does not lie (usually). He might exaggerate the truth, speak in an open code or leave out info but he doesn't just lie which is what you are suggesting.
If you have to resort to #3 or #4 (as you described it, not with the additions I described) its time for you to get rid of the character your not a good manipulator and shouldn't by trying this sort of thing. It will a better game if you play to your strengths as a GM and not try things that end up making the players mad.