I made a small example, which basically does the same as your code, and I show that the expected results are obtained:

### Imports

    In [1]: from keras.models import Sequential
    In [2]: from keras.layers import Dense

## Build a model

Note the `name` arguments:

    In [3]: model = Sequential()
    In [4]: model.add(Dense(50, input_shape=(20, 20), name='dense1'))
    In [5]: model.add(Dense(30, name='dense2'))
    In [6]: model.add(Dense(1, name='dense3'))
    In [7]: model.compile('rmsprop', 'mse')
    In [8]: model.summary()
    _________________________________________________________________
    Layer (type)                 Output Shape              Param #   
    =================================================================
    dense1 (Dense)               (None, 20, 50)            1050      
    _________________________________________________________________
    dense2 (Dense)               (None, 20, 30)            1530      
    _________________________________________________________________
    dense3 (Dense)               (None, 20, 1)             31        
    =================================================================

## Rename the layers

    In [9]: for i, layer in enumerate(model.layers):
        ...:     layer.name = 'layer_' + str(i)
    In [10]: model.summary()
    _________________________________________________________________
    Layer (type)                 Output Shape              Param #   
    =================================================================
    layer_0 (Dense)              (None, 20, 50)            1050      
    _________________________________________________________________
    layer_1 (Dense)              (None, 20, 30)            1530      
    _________________________________________________________________
    layer_2 (Dense)              (None, 20, 1)             31        
    =================================================================

So we see the layers now have the new names!

## Further inspection

I can see that the internal identifiers of the layers themselves **are not changed**. I show the first layer's weights, as we see the original label is still present:

    In [11]: a = model.layers[0]
    In [12]: a.weights
    Out[12]: 
    [<tf.Variable 'dense1/kernel:0' shape=(20, 50) dtype=float32_ref>,
     <tf.Variable 'dense1/bias:0' shape=(50,) dtype=float32_ref>]

We see the `dense1` name is still visible in the layer container, along with its unchanged shape and datatype.

I also initialised the model weights by running `model.get_weights()`, then renamed the layers as before to new names, compiled the model and saw that the layers' names were altered as before, and the weights themselves were not changed i.e. reinitialised. The exact same values were contained. This means that renaming your layers cannot be behind the drop in accuracy.