I would use a mulch of biggish pebbles and let the dog have that spot for his social life. Plant somewhere else.

James Stirling (they call them something else nowadays) pittostriums - they are very hardy and you can grow them in a thin garden bed (but will need to water if thin). You can let them go or trim them to what you like. You can buy them small and they grow quickly so it isn't expensive. I have them growing in a narrow bed (15-20cm) near a pool and I keep them very thin due to pool regs. I then did some underplanting of black & green mondo.

my fence is painted black as well so it allows the green from the plants to pop.

Nandina would make a lovely all year round display of colour along the fence.

As suggested by Scott - a wire trellis with a climber. Star Jasmine would compliment the Nandina.

Both of course, can be trimmed to keep under control.

Nasturtiums - can hang down or have something for them to climb up the fence. Wire? Trellis?

Mint - grows pretty much anywhere! Strawberries, my dog loves to sit between them.

Native plants are great.

For the pup you could put a "window" peephole in the fence, for socialising with other dogs. Be careful what you plant, many plants can be toxic to inquisitive pups.

Sorry puppy there's a time and place for everything. ..some rules will need to apply. Contain an are where he gets to sprint across the yard and a sunny position for him to sit but vegetation is needed including hanging plants that cascade over the front of the garden bed... puppy will survive as will joy as there will be plants