Sharepoint - Replacing the Office 365 logo and link in Sharepoint Online Suite Bar

You can try this solution:

1. Open your site in SharePoint Designer, check out and open the default masterpage in advanced mode (assume it is seattle.master).
2. Scroll down to ending </body> tag.

3. Add the following block of code above:

   <SharePoint:ScriptBlock runat="server">
   if (typeof jQuery == 'undefined') 
   {
   document.write('<script type="text/javascript" src="//code.jquery.com/jquery.min.js"><' +         '/script>');
   }
    var interval = setInterval(function(){
   if($('#O365_MainLink_Logo').length)
   {        
   $('#O365_MainLink_Logo').html("<a href='/'><img src='/SiteAssets/YourLogo.PNG' height='25px'></a>");
   $('#O365_MainLink_Logo').attr("style","padding-top: 3px");
   clearInterval(interval);                
   }
   }, 1000);    
   </SharePoint:ScriptBlock>
   

4. Upload logo image file you want to use (i.e. upload to Site Assets library).

5. Save the edited masterpage, check it in.

6. Reload your site.

Credits to this site

At the moment, you would need to use jQuery. However, the Suite Bar in SPO has changed numerous times, so be prepared to make changes in response to those changes.

The ability to customize the Suite Bar has been suggested in UserVoice. I suggest you add your vote there.