I always think that the name "Reine Claude" makes them taste betterer
Me too, but UK forum & all that. As it happens, I didn't know that Reines Claude were greengages until the missus's folks moved here.
"Greengage" begs to be followed by "jelly". Dunno if it's still the case, but when I was a nipper almost all homegrown fruits ended up that way. We had raspberries, gooseberries, and black & red currants and rhubarb, and they all met with me mum's preserving pan, apart from the ones we snaffled in the garden. If she could have made jam from broccoli we'd probably have had dark-green jars of stinking puke on the breakfast table.