Final answer:
George Takei was named after King George VI of the United Kingdom. The reasons behind the naming of his siblings Henry and his sister are not publicly known.
Step-by-step explanation:
George Takei, an actor and social activist, was named after King George VI of the United Kingdom. This was revealed in George Takei's 2014 TED Talk, where he discussed his childhood experiences as a Japanese American during World War II, including his time in a Japanese internment camp. Takei's tale is one of resilience and patriotism, despite the injustice he and his family faced. Regarding the names of his siblings, based on available information, it seems that the specifics behind the naming of George Takei's brother Henry and sister have not been publicly disclosed.