Rename the main product and its child products after being cloned.

[MP]

Hello,
I made a product with price variations that vary according to 2 factors: material and size.
Obviously I used the custom field: multi variant.
The prolema was born when, I have to create a new product with the same characteristics but with only the different image and name.
In fact, I clone the product with the children (clone product Tree), I change the image, I rename the product,
but the name of the children remains the same as the first product, the original one.
In this way the name of the children I find it in the product sheet when the customer goes to choose the desired variant
and in the cart once the product has been chosen.

What do you suggest to me to avoid doing a long job of renaming all child products?

Thanks!