I have 2 Home page links

Some themes - such as Contempt, Cutline, Light and others - have a bar in which Page titles appear.

If you then choose to have a static page you can end up with 2 Pages in that bar which go to the same place - the front of the blog.

To fix that, go to Manage > Pages and edit the Page you have chosen to be the front page.
Look down the page for the ‘Page Parent’ box.
Open it and make that page the child of the Posts page you chose - so make the Posts page it’s Parent.

That will hide the Page title.

Note:
This may not change  how the  pages/tabs are displayed in that bar
If you are using the Pages widget the front page will still show there.

If you do not use the Pages widget and the child page is not linked from anywhere else, if you stop using it no-one can see it.