Rename and move images to a destination directory based on a text file followup
You have lots of unneeded empty lines, they also hinder readability.
fn(arg=value) is abnormal. It's common to use fn(value). It's common only to use the former when the argument is a keyword or default argument.
You don't need to make a path another path.


desination_root = Path("R:\\Pictures")
destination = Path(desination_root).joinpath(folder.stem)


Path.mkdir isn't a static method, and so it's abnormal to use it as Path.mkdir(my_path) rather than my_path.mkdir().
check_if_folder_exists isn't needed as repository.iterdir and destination.mkdir will error if they don't exist.

It should also be noted that you can pass parents=True to Path.mkdir to automatically create the folder if it doesn't exist, rather than force the user to do that.
It's better if you make another function that moves the files, and one, main, that passes it the values. Preferably main would be changed to not use static values and get the values from a config file.
finally isn't needed.
You should raise a SystemExit(1) or use sys.exit(1) if there is an error. They both do the same thing which notifies the system that the program failed. It didn't run without problems.
Given that generating a name that doesn't conflict with existing files is not a simple one-liner I'd recommend you move it out into a function.

I should note that it may overwrite files, if you have a folder with file_1.png and file_3.png your code's going to overwrite file_3.png, but not have a file_2.png.


You changed away from some of the above, and so I'd recommend you think about the differences, which is easier to re-use, which is easier to read, which performs the correct action in the situation. If you don't know what the difference is even with my explanation, such as with SystemExit(1), then you should look up what it does.

import os
from pathlib import Path
import shutil


def gen_name(path, number):
    orig_name = path.parent.name.lower().replace(" ", "_")
    return f"{orig_name}_{number}{path.suffix}"


def move_files(src, dest):
    for folder in Path(src).iterdir():
        destination = Path(dest) / folder.stem
        destination.mkdir(exist_ok=True, parents=True)
        start = len(os.listdir(destination)) + 1
        for number, image in enumerate(folder.iterdir(), start=start):
            image_name = gen_name(image, number)
            destination_image = destination / image_name
            print(f"{image} will be named {destination_image}")
            shutil.move(image, destination_image)


def main():
    try:
        move_files(
            "{0}\\{1}".format(os.getenv("USERPROFILE"), "Repository"),
            "R:\\Pictures",
        )
    except(ValueError, FileNotFoundError, OSError) as error:
        print(error)
        raise SystemExit(1) from None


if __name__ == '__main__':
    main()


I think it could make more sense for gen_name to be a closure, as then it can correctly handle existing files. I won't change how the code functions, but will show how it could be implemented.

def gen_name_builder(folder):
    orig_name = folder.name.lower().replace(" ", "_")
    number = len(os.listdir(destination))
    def gen_name(file):
        nonlocal number
        number += 1
        return f"{orig_name}_{number}{path.suffix}"
    return name


def move_files(src, dest):
    for folder in Path(src).iterdir():
        destination = Path(dest) / folder.stem
        destination.mkdir(exist_ok=True, parents=True)
        gen_name = gen_name_builder(destination)
        for image in folder.iterdir():
            image_name = gen_name(image)
            destination_image = destination / image_name
            print(f"{image} will be named {destination_image}")
            shutil.move(image, destination_image)