So I did a bit of reading, and I'm probably more confused now. The official version of the background to the Charing Cross in London is that it takes its name from one of the Eleanor Crosses erected by Edward I in memory of his wife - the one in the old parish of Charing, in fact, the most southerly of the twelve crosses, which were placed in a very approximate line at sites between London and Lincoln. The name Charing is thought to be derived from the Old English "cierring", referring to a nearby bend in the River Thames.
|There's another one|
So I got to thinking, maybe a Charing Cross is a more general thing - some kind of cross (obviously), serving some community purpose, or commemorating something more general than Eleanor. That didn't get very far. One interesting fact is that there seems to have been an important Charing Cross Hotel at both the Glasgow and Birkenhead locations - you don't suppose they were just named after the place in London? Might they have been railway hotels? Hmmm.