I'm curious why "bl_anode" is shown connected to the "cathode" of the diodes and the two "bl_cat1/2" are shown connected to the anode sides?
"BL" possibly means "back-light" and maybe it is a device that uses an anode and a cathode. Hence the net-name sounds fine to me and has zilch to do with D4020 and D4021.
Another hint is the "LCM" might stand for liquid crystal module i.e. a module containing a liquid crystal display AND a back light.
It looks like the labels you are referring to are with respect to the rest of the circuit. Basically, this is a power supply, and its outputs are intended to be connected to cathodes and anodes of other things. The fact that internally the cathodes of diodes are connected to the "anode" output is immaterial.
This is how a cellphone display backlight gets it DC supply from a step-up switchmode power supply. Actually there are two parallel power supplies with different inductor sizes to choose from for adjustable brightness.
BL anode is the anode of the background light source (not drawn here). The diodes are fast schottky diodes that belong to the step-up switch mode supply circuit. In that switchmode topology the +output comes from the cathode of the diode.
Addendum: The parallel supplies produce a current pulse in their turn to the output. The current pulses carry different size charges. Output capacitor keeps the output voltage quite stable (=no flashes and minimal radio interference). By interlacing a proper ratio between big and small pulses the average current is as wanted. No reason, why the supplies can't operate even at the same time. But to be sure, a datasheet is needed. I haven't found one.
Step-up principle is used to bring the wanted charge into proper voltage level for many leds in series. Cellphone battery has too low voltage as-is.