Having 2 partitions with the same name and/or device name can cause issues but shouldn't affect booting.
Booting into AmigaOS (aka the other kind of 3.x ;) ) is more likely due to it having the same or higher BootPri as your main boot partition.

Programs asking for "DH0:" instead of going for "SYS:" are just badly coded and should be fixable by adding an assign.


My advice:
Setup the CF card with non conflicting device and volume name and make sure the BootPri is in clear favour of the MorphOS partition.

If you don't plan to transfer files with this card later just change everything to normal names once booted into AmigaOS on the A500.


Otherwise I would suggest adding the assigns there to fix broken SW.