I recently noticed that
teammate is composed of two anagrams, and was wondering if anyone had any other examples of this, or even better, a name for this phenomenon?
"Teammate" is a compound word -- composed of two simpler words. "Team" and "mate" are coincidentally anagrams of each other, but there is no reason for this phenomenon to be "named", as it carries no significance, either in meaning or etymology.
There is probably a slight tendency for such anagram pairs to be joined into a compound word due to the increased likelihood they will have of being assonant with each other (making their use together more likely in idiomatic speech), but this is not what you would call a notable characteristic.