老师 = a respectful term to mean teacher. 老子 = old man or Lao Tzu 老字 = old/obsolete/ancient character 天名 = literal meaning heavenly/celestial name. As a term, no meaning at all without context.

老子 could either be the great philosopher of Taoism or I/ me/myself ( it's an arrogant or rude way of saying that), but the tone of 子 is different.