By default, a SharePoint logo does not redirect the user anywhere upon clicking.
Moreover, making the logo clickable is not possible with SharePoint tools, and requires programming.
Fortunately, with ShortPoint Theme Builder, you can link your logo to any page inside or outside your organization.
Here's an example of how a user is redirected from the company's Legal Department page to the main Homepage after they click the logo:
If you want to implement the same on your site, please continue reading this article.
STEP 1. Open ShortPoint Theme Builder.
In SharePoint Online, please navigate to Site Contents > ShortPoint > Site Customizations > Customize my Site.
In SharePoint On-Premise 2013/2016, go to Site Settings > ShortPoint Dashboard > Site Customizations > Customize my Site.
STEP 2. Navigate to the Logo Settings.
In the Theme Builder, click Header > Logo:
STEP 3. Assign the Link to the Logo.
Copy the URL you would like the logo to redirect the users to.
In the Logo Custom Navigation Link field, paste the URL: