What is the term for the use of two words of the same meaning consecutively?

sadly this has an actual term, even the show host was taken back.

Those are pleonasms — instances where there's a word or two more than necessary. A pleonasm is a type of redundancy, though not one in which the words mean exactly or nearly the same thing.
http://nhpr.org/post/please-dont-have-temper-tantrum-about-pleonasm-headline

pleonasm is the word

Pleonasm is using more words than you need to, either accidentally or deliberately.

An example of pleonasm? "She picked up the tiny little baby kitten."

The Greek root word in pleonasm is pleonazein, which describes something as more than enough. Used accidentally, a pleonasm is just long-winded wordiness, like a sentence that includes far more words than is necessary. Used on purpose, pleonasm is a tool used by writers and speakers to emphasize something or clarify an idea through repetition. This helps audiences remember main ideas as they listen or read.

the closest thing that came up is pleonasm, but that doesn't fit the use of safe haven. where both words mean the same thing but are used together to make one word.