Crossbar is the most descriptively accurate.
Tommy bar and Pin Handle tie for "Hand you a what?"
It depends on what kind of shop you're standing in!
This has come up periodically here and we touched on the terminology (and etymology) aspects in an older thread on hinge or flex-head handles that turned into a 'Crossbar' thread, linked
here. "Crossbar" is demonstably the most common term in vintage automotive mechanics hand tools literature (catalogs, manuals, etc). Terms such as "tommy bar", "tommy-bar", "tommy wrench", "pin wrench", and "pin handle", all as old as the late 1800's, have leached into discussion here from the machinery world, for turning (or holding steady) all kinds of pieces drilled with holes known as tommy or pin holes, and can still be found in modern technical literature with respect to lathes, mills, etc, and even C-clamps.
In a broad (though I wouldn't claim exhaustive) search of all major hand tool mfgr's catalogs in the 1930's, I found that none were using "tommy bar", Plomb was the only one using "pin handle", and all the others were using crossbar. The Federal Standard Stock Catalog at that time (which has evolved into the NSN system) used cross bar, technically, "Bar, cross".
The biggest crisis is not their terminology, but their size. As everyone knows, they are almost always MIA, a good practice for all pickers is to never leave them any of them behind, but not all of them are interchangeable across mfgrs! Good summary
here.