aptagram
n. An anagram in which the new word or phrase has a similar meaning to the original word.

Example Citations:
That would, of course, be an astronomer (which is an aptagram of astronomer — an anagram with a similar meaning)!
—Ten Tibias, “What is a moon starer?,” Answers.com, January 23, 2009

After the formal introductions, the General cupped his hand to his mouth and whispered in Dmitri’s ear in a gesture of fraternal bonhomie. ‘Anna gives great anagrams. She can sit on my emordnilap any day. Gramsci comes up with aptagrams for the names of countries and their citizens. Go on. Take her for a spin.’

’United States of America,’ declared Dmitri. ‘I, SAM, STUNT, ERADICATE FOE,’ she replied.
—John Holgate, “A day at the You knighted nay shuns,” Word Ways, November 1, 2005

Earliest Citation:
But it is even more fascinating when we reconfigure words into other words that bear a meaningful relationship to the base. These significant tandems are called aptagrams—words that anagram into their own synonyms.
—Richard Lederer, “Looking at language; Check out this ever-changing parade of antigrams,” The Patriot-Ledger, March 22, 1997

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