Changing the theme name to a random name is possible by creating a child theme that extends the Pearl Theme. That can be implemented by following magneto documentation on how to create a child theme.
If it's easier for you, you could use the child theme that already comes with Pearl Theme pack by following the steps below;
1. Go to the child theme that is already created under /app/design/frontend/Pearl/weltpixel_custom and copy it under a new location, for example: /app/design/frontend/MyTheme/my-theme/
2. Go to /app/design/frontend/MyTheme/my-theme/theme.xml and modify the theme title from 'Custom Pearl Theme for Magento 2' to "Random Name Theme" so you can recognize it in the Magento admin. Do not change the parent theme, keep it Pearl/weltpixel.
<theme xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:Config/etc/theme.xsd">
<title>Random Name Theme</title>
3. Go to /app/design/frontend/MyTheme/my-theme/registration.php and change the newly created theme path from 'frontend/Pearl/weltpixel_custom' to 'frontend/MyTheme/my-theme'
4. Go to the Magento Admin and set your new child theme as the currently active theme.
5. Go to the Cache Management section, regenerate the LESS/CSS files and flush the Magento Cache.
6. Go to developer mode, do a static content deployment.
php bin/magento deploy:mode:set developer
php bin/magento setup:static-content:deploy -f
php bin/magneto cache:flush
7. Check your storefront. Just click Inspect -> View page source. You should be able to see the files loaded under your new theme name.