You really can't even make a choice here without determining the PHY layer but some ideas:
If the system really is daisy chained as drawn then bring up each device in order. Factory program to the "broadcast address" if the PHY has one (like I2C does). Then just have each device pick an address and send that address to the next device as it moves down the chain.
If use 8bit UIDs, you get bonus points, at least from me, if you spell something comical in ASCII with the addresses:
Master: "Hey device 1, choose an address"
Device 1: "M", hey device 2 choose an address
Device 2: "y"
Device 3: "B"
Device 4: "o"
Device 5: "s"
Device 6: "s"
Device 7: "S"
Device 8: "u"
Device 9: "c"
Device 10: "k"
Device 11: "s"
Alternatively if your design has a fixed number of devices: I had a design that used a backplane that allowed up to 4 cards to be plugged in. What i ended up doing what placing a I2C based GPIO expander on the backplane (actually it was a fan control IC i needed anyway, i just picked one with and I2C interface and some GPIOs on it).
I routed a GPIO through each card edge connector to the reset pin of the DSP on each plug in card. All DSPs were factory programmed to 1 address. The system controller brought the slots out of reset 1 at a time, an I2C command was sent, if something ACKed it was assumed the slot was populated and a command was sent for it to change its I2C address to a UID for that slot. This was done for each slot with a reasonable reply time out.
If its a shared bus that capable of slave initiating transfers, aka multi-master. Just have the slave device assert control of the bus and ask the master for an address, master just gives it the next address in line, think DHCP. Same bonus points as above.
If the PHY is single master and you have a completely unknown number of devices....daisy chain a GPIO through them and use that to control if they respond to a factory programmed address? Then when the slave gets its address, it de-asserts the next device in line? This way you only need 2 GPIO pins per device and 1 for the master and you can bring devices up one at a time. Should work i think.
Anyway, honestly all speculation till you choose a PHY and can tell us more about how the overall system is connected.