"He told me his name was" VS "He told me his name is"

When considering the following example:
"I met a man yesterday. His name is John"
I understand the idea behind using "is" instead of "was" - here, arguably, the condition is permanent (somebody's name does not change and is true for all times, rather than a specific time).

However, when considering the following sentence:
"I met a man yesterday and he told me that his name was/is John" 
The past tense seems like a more sensible/fluid option. Many study materials (specifically, for the GMAT exam) claim that the correct tense would still be the present "is", since John's name will not change. What is the correct/logical structure here?

Also, would it change for the following cases, for example:
"I met a man yesterday and he told me that the sky was/is blue"
"I met a man yesterday and he told me that he was/is a musician"
"I spoke to a man yesterday and he insisted that he was/is old"
"I spoke to a man yesterday and he informed me that he was/is a WW2 veteran" 


Apologies for such a long question; I am just trying to understand the logic here.

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