Your styles don’t look that different as per PP.
Max - Maxwell?
Luca - Lucas?
Zachary - Zachariah?
Jude is definitely a boys name and does it matter if some people think it sounds feminine? Lots of females around called Max and Luca too.
Edward is pretty classic but also very popular. It’s top-25 on its own but with Teddy also in the top 30, if you combined the two it’s a top-5 name, more popular than Leo (even more I imagine if you added in Eddie, Eddy, Teddie, Ed and Ted)
If you wanted something a little less popular so you are less likely to run into one as a teacher - perhaps go outside the top 100? Tobias, Dominic, Robert, Nathaniel, Wilfred, Christopher, Owen, Lewis, Luke.
Or from outside the top 250? Franklin, Fletcher, Nicolas, Barnaby, Douglas, Hector, Casper, Nico.
I also teach and I chose names from outside the top 1000 for all my DC.