The original affiliate link cannot be changed but you can create a custom affiliate link (for example: shopurl/affiliate name) by creating URL redirect on your shop Admin on Shopify.
For example, affiliate link would normally look like:
But you can create redirect link which looks like this: https://shopurl/michelle
Go to your shop admin => click on Online store => Navigation
2. Click on URL Redirects
3. Click Create URL redirect (or you can click import redirects for bulk action)
4. On Redirect from, fill in the custom link you want to show to customers
On Redirect to, enter the generated affiliate link
Then click Save redirect to save change.
After saving, you can test the redirect by visit the custom link, it should immediately redirect to the original affiliate link.