It's pretty complicated because different systems call them different things.
Some systems always refer to the 2nd TE as a "U" and the 3rd WR as a "S".
In our case I think we're to interpret that the 2nd TE, the guy who moves around, resets, shifts, is generally more mobile, etc...is an "F". And the #1 TE is a "Y".
Where that runs into issues is now you're also saying there's an "H" and to my knowledge the "H" by definition has to be a backfield player, can't be on the line. Some systems refer to the slot receiver as an "H".
I think you can have both the "F" and the "Y" up on the line of scrimmage for example in an "Ace" formation (which has tight ends outside the left and right tackles, up on the line, with a wide receiver to either perimeter, both wide receivers a yard off the line of scrimmage).
As you say, the "X" and the "Z" are a bit easier to figure out.