The HTML heading one element (<h1>) must exist because it is the most visible title on your page. The <title> markup is less visible for the users because it is available on the tab of a browser. Also, the text within it is for search engine bots. But the <h1>'s text is for your users.
There must be one <h1> element on every page of your website. You must not have two of it. Have one <h1> element. Having two HTML heading one elements is like having two titles for a novel. A novel should only have one title. If it has more than one title, the writer is abnormal.
The heading one should act as a title of your page. This means it should not be used for your logo. It should not be used to make the biggest text on a page. It should not be used for anything other than a title.