* Do not use capitalization for function names. This violates idiomatic python naming conventions ([PEP8 link](https://www.python.org/dev/peps/pep-0008/#function-names)). Try out [pylint](https://www.pylint.org/) to catch these kinds of issues
* Prefer `str.format()` over concatenation. `str.format()` is not only a lot more flexible, but easier to use than concatenation and more efficient for combining more than 2 strings. `str.format()` you do not need to explicitly convert objects to the string type (less `TypeError` exceptions). Instead of `str(name) + ".jpg"` do `"{}.jpg".format(name)`
* Use sub functions to break up your code. This function is on the larger side.
* Prefer iteration over indexing. A `list` or any container can be iterated over to yield its contents. For example do `for link in links_list:` instead of `while k <= (len(links_list) - 1):`

Randomly picking a filename is decidedly not a good idea. The given filename may already exist, and urlretrieve will go ahead and overwrite the file.

Here's would be an example function for retrieving a unique filename.

    from itertools import count
    
    
    def unique_filename():
        """Yield a unique filename.

        The given filenames start at 0.jpg, 1.jpg and so on
        """
        for filenum in count():
            filepath = "{}.jpg".format(filenum)
            if not os.path.exists(filepath):
                yield filepath


then you could do something like:

    for link, filename in zip(links_list, unique_filename()):
        urllib.urlretrieve(link, filename)

We use a generator to yield only filenames that do not exist, and use the finite `links_list` to limit the generator since `zip` stops when the first iterable is exhausted.

As a side note, `links_list` is a very redundant name. A list implies multiple. I (and [Brandon Rhodes](https://www.youtube.com/watch?v=YklKUuDpX5c)) would rather name it `link_list`. If this was ruby, you would want to just name it `links`.

Lets pull out the link finding code into its own function.

    def image_links(soup):
        """Yield src tag jpg urls from given BeautifulSoup object."""
        for link in soup.findAll('img'):
            image_links = link.get('src')
            if '.jpg' in image_links:
                for i in image_links.split("\\n"):
                    yield i.split()[0]

I do have a suspicion that some of these splits are not needed.

We can also pull out the html tree object creation code into its own function:

    def get_soup(url):
        """Get BeautifulSoup object from given url.

        Does not do any error checking.
        """
        source_code = requests.get(url)
        plain_text = source_code.text
        return BeautifulSoup(plain_text, "html.parser")


Bringing these functions together we get an easier to understand main function:

    def download_images_from_page(url):
        """Download jpg images from html at given url to the local filesystem.

        The use the cwd for the location of the downloaded images."""
        soup = get_soup(url)
        for link, filename in zip(image_links(soup), unique_filename()):
            urllib.request.urlretrieve(link, filename)
            print(link)
            print("{}\n".format(filename))