When the PayPal transaction is complete, PayPal shows this:
Thanks for your order
Your payment of $XXXX.XX USD is complete.
You\'re now going back to MYSITE.
What you ask is achievable with PayPal Payments Standard, but the seller account receiving the payment needs to be a PayPal Business/Premier account (a free upgrade), and they need to enable Auto Return and provide a Return URL in their PayPal account > Profile > Profile & Settings > My Selling Tools > Website Preferences.
You can also pass a return
URL variable to checkout for each order, which would override any Return URL (or lack thereof) in the seller's PayPal account profile; however, if Auto Return is not also enabled in the seller's account, the buyer would need to click past the end of checkout manually in order to be redirected to that URL.
Check out https://developer.paypal.com/. You can build your own interface using PayPal's API. The user will never know that PayPal handled the transaction.
Be sure to review PCI-DSS requirements when using this approach.
You will also need a Website Payments Pro subscription for that. https://www.paypal.com/webapps/mpp/website-payments-pro
Once you have it, get the API signature, API username & API password from the My Profile area of your paypal account.
Then, use the Direct Payment method as described in the following manual https://cms.paypal.com/cms_content/US/en_US/files/developer/PP_WPP_IntegrationGuide.pdf
As mentioned by Watermark, you might need to review PCI requirements and at least have SSL on your site before you can do this.