Batch rename of files that share the same prefix

I have a list of files on my server with a prefix that I want to de-dupe. These are completely different generated files. It seems to be generated files with

{Title} - {yyyy-MM-dd}_{random} - {Description}.ts

For example:

Camera Recording - 2023-08-11_14 - Front Deck.ts
Camera Recording - 2023-08-11_14 - Back Deck.ts
Camera Recording - 2023-08-16_27 - Front Deck.ts
Camera Recording - 2023-08-16_36 - Front Deck.ts
Camera Recording - 2023-08-17_56 - Front Deck.ts

I need to be able to run a script that identifies duplicate prefixes of the following filesnames. Then changes the number prefix {random} part after the date

Camera Recording - 2023-08-11_14 - Front Deck.ts
Camera Recording - 2023-08-11_14 - Back Deck.ts

To become the following, the {random} needs to be replaced with a different value (other than 14)

Camera Recording - 2023-08-11_14 - Front Deck.ts
Camera Recording - 2023-08-11_68 - Back Deck.ts

Any advice on how to achieve this with a linux shell script?