I have following saved_model dir structure. The saved_model_cli is working correctly with the path but docker command not. Note this is following the book example and apparently docker part of example not working.
test.npy test input feeds 3 instances of mnist 28x28 images to serving.
DIR STRUCT:
root@nonroot-Standard-PC-i440FX-PIIX-1996:~/dev-learn/gpu/tflow/tensorflow/tflow-2nded# tree p297
p297
├── 0001
│   ├── assets
│   ├── saved_model.pb
│   └── variables
│       ├── variables.data-00000-of-00001
│       └── variables.index
├── assets
├── keras_metadata.pb
├── saved_model.pb
└── variables
    ├── variables.data-00000-of-00001
    └── variables.index

CLI:
    saved_model_cli run --dir p297/0001 --tag_set serve --signature_def serving_default --inputs 
flatten_input=test.npy

output of cli (OK)
2021-11-08 15:57:11.458910: I tensorflow/core/platform/cpu_feature_guard.cc:142] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations:  SSE3 SSE4.1 SSE4.2 AVX AVX2 AVX512F FMA
To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.
2021-11-08 15:57:11.460906: I tensorflow/core/common_runtime/gpu/gpu_device.cc:1510] Created device /job:localhost/replica:0/task:0/device:GPU:0 with 31740 MB memory:  -> device: 0, name: Device 738c, pci bus id: 0000:00:07.0
WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/tensorflow/python/tools/saved_model_cli.py:445: load (from tensorflow.python.saved_model.loader_impl) is deprecated and will be removed in a future version.
Instructions for updating:
This function will only be available through the v1 compatibility library as tf.compat.v1.saved_model.loader.load or tf.compat.v1.saved_model.load. There will be a new function for importing SavedModels in Tensorflow 2.0.
INFO:tensorflow:Restoring parameters from p297/0001/variables/variables
2021-11-08 15:57:11.961912: I tensorflow/core/common_runtime/gpu_fusion_pass.cc:507] ROCm Fusion is enabled.
2021-11-08 15:57:12.671939: I tensorflow/core/common_runtime/gpu_fusion_pass.cc:507] ROCm Fusion is enabled.
2021-11-08 15:57:12.686081: I tensorflow/core/common_runtime/gpu_fusion_pass.cc:507] ROCm Fusion is enabled.
Result for output key dense_2:
[[3.65022061e-05 2.47262960e-05 6.37578269e-05 2.08125566e-05
  7.02261750e-05 1.18829332e-01 4.30839646e-05 2.72816449e-01
  1.48763061e-02 5.93046188e-01 6.37045162e-07 3.02645799e-06
  3.80635288e-06 4.22269186e-05 6.12226586e-06 4.33605646e-06
  7.58367719e-07 3.06199559e-06 5.42078442e-06 2.38417056e-06
  4.93106018e-06 7.25027712e-06 1.24132812e-05 1.24427579e-05
  1.15528803e-06 4.87520847e-05 1.68714314e-06 8.28819338e-07
  2.23448342e-06 9.11506140e-06]
 [1.64286757e-04 3.39760754e-06 9.66621459e-01 1.61247503e-04
  1.02249524e-02 7.44288286e-07 2.27110237e-02 3.17756710e-10
  1.12835020e-04 3.98790796e-08 4.89366492e-10 1.29820976e-09
  9.63464334e-13 5.25168797e-10 9.53418247e-11 4.82374418e-10
  2.60897762e-11 2.75338996e-12 3.59164387e-09 7.25419169e-11
  5.41757861e-10 8.33503266e-10 1.25494719e-11 4.14474233e-09
  3.54530544e-10 7.37128275e-11 4.25408209e-10 7.22836443e-11
  6.95292546e-10 2.50320233e-11]
 [1.12954825e-04 9.99067128e-01 5.11940962e-05 5.15281979e-04
  2.25681084e-04 7.90114484e-07 2.39875553e-05 1.08763277e-06
  6.77304740e-07 8.83030324e-08 3.44932758e-08 3.36465895e-08
  1.49800372e-09 2.67271858e-08 7.71939810e-08 1.00484840e-07
  5.05017761e-09 4.95800823e-09 1.20519260e-07 1.41827059e-07
  1.35087987e-07 3.95625591e-07 4.27236913e-08 4.71499533e-08
  3.37586954e-08 1.78841599e-08 1.00948716e-08 4.40149028e-10
  2.45303022e-09 2.79508638e-09]]

DOCKER:
    MODEL_NAME=p297
    docker pull tensorflow/serving
    docker run -it --rm -p 8500:8500 -p 8501:8501 \
        -v "$MODEL_NAME:/models/$MODEL_NAME" \
        -e MODEL_NAME=$MODEL_NAME \
        tensorflow/serving

output of docker instance (fail):
Using default tag: latest
latest: Pulling from tensorflow/serving
Digest: sha256:6651f4839e1124dbde75ee531825112af0a6b8ef082c88ab14ca53eb69a2e4bb
Status: Image is up to date for tensorflow/serving:latest
docker.io/tensorflow/serving:latest
2021-11-09 00:01:43.627821: I tensorflow_serving/model_servers/server.cc:89] Building single TensorFlow model file config:  model_name: p297 model_base_path: /models/p297
2021-11-09 00:01:43.628201: I tensorflow_serving/model_servers/server_core.cc:465] Adding/updating models.
2021-11-09 00:01:43.628227: I tensorflow_serving/model_servers/server_core.cc:591]  (Re-)adding model: p297
2021-11-09 00:01:43.629366: W tensorflow_serving/sources/storage_path/file_system_storage_path_source.cc:268] No versions of servable p297 found under base path /models/p297. Did you forget to name your leaf directory as a number (eg. '/1/')?
2021-11-09 00:01:44.629551: W tensorflow_serving/sources/storage_path/file_system_storage_path_source.cc:268] No versions of servable p297 found under base path /models/p297. Did you forget to name your leaf directory as a number (eg. '/1/')?
2021-11-09 00:01:45.629769: W tensorflow_serving/sources/storage_path/file_system_storage_path_source.cc:268] No versions of servable p297 found under base path /models/p297. Did you forget to name your leaf directory as a number (eg. '/1/')?
^X2021-11-09 00:01:46.629997: W tensorflow_serving/sources/storage_path/file_system_storage_path_source.cc:268] No versions of servable p297 found under base path /models/p297. Did you forget to name your leaf directory as a number (eg. '/1/')?

I logged onto container using
docker-exec -it <C_ID> /bin/bash
and inspected p297/0001 folder but turns out to be empty.