Most Joomla developers will want to remove the title tag from the home page text where it shows up as an H1 tag on the top of the body / article area. Removing this from the home page will not affect the actual title tag, which is one of the most important items used in search engine optimization, but it will clean up the home page as H1 tags can be very large and can easily distract site visitors from the content of your site.
Many people feel that having H1 tags on individual pages can help with search engine optimization, but recently, representatives of some of the large search engines have been down-playing this by saying that the H1 tags no longer carry the weight they once did. It's up to you whether or not to keep the tags, but if you would like to remove them, I will explain how to do so.
I'm going to assume that you have a recent version of Joomla installed and understand how to access the administration area and are familiar enough with it to make changes to the site.
First, you will want to log on to the administrator area of your site. Next, go to the "Menus" menu and choose "Main Menu". Now click on the "Home" link, or if you have changed the name of the link, choose the name that has a gold star in the "Default" column.
Next you will want to click on "Parameters (System)" located on the right side of the page. Finally, locate "Show Page Title" and click on "No" then click "Save". Now return to your home page and you will notice that the Title tag no longer displays on the top of your site.