MARK B. answered 07/15/19
SAT Writing instructor with 16 years of highly successful experience
Yes--at least, at first mention in your piece--because otherwise the reader may assume that is his ENTIRE name. AMBIGUITY. No rules when it comes to personal names--they can be spelled, or pronounced, ANY DARN WAY folks choose. So a little "dot" clears things up--no more AMBIGUITY: We then know that he's got a full name beyond "T."
Here's how you might do it in your masterpiece = first time, write Uncle T(ooboringtoinvitetoourfamilygettogethers). Thereafter, Just Uncle T, and you then won't need the "dot."