Lets say we have our own script here:
// Code inside the script.php
$url = 'https://foo.com';
$ch = curl_init();
curl_setopt($ch, CURLOPT_URL, $url);
curl_setopt($ch, CURLOPT_HEADER, 0);
curl_setopt($ch, CURLOPT_RETURNTRANSFER, 1);
curl_setopt($ch, CURLOPT_CONNECTTIMEOUT, 30);
curl_setopt($ch, CURLOPT_TIMEOUT, 60);
$data = curl_exec($ch);
As you can see, the link above gets content of this domain:
I know foo.com can see example.com and it's IP Address!
but Questions is, can foo.com (the page we're getting content from) also by any methods detect this exact part: /random_name/script.php is making the request? does it depend on using TLS?
The page (server/application) can have all the information in the request. If the request (in your example - script.php) will not send the extra data (/random_name/script.php) the page the receive the request will not have it.
If you want to receiving end (foo.com) to know about it you can use the referer header:
curl_setopt($ch, CURLOPT_REFERER, "https://example.com/random_name/script.php");
And this way - foo.com can view that information in the referer header.