<title> is a required element on any HTML page to be valid markup, and will be what is displayed as the page title in your browser’s tab/window title. For instance, try inputting the following markup into the W3C Markup Validator (via “Direct Input”):
<!DOCTYPE html>
<html>
<head></head>
<body></body>
</html>
This will produce an error that there is no instance of <title> in <head>.
The <meta name="title" content="page-title"> element is just that — metadata about your page, that any client browser or web crawler can use or not use as it wants. Whether it is used or not will depend on the crawler/client in question, as none of them are required to look for or not look for it.
So in short, you should have a <title> element if you want valid markup. The <meta> tag is going to depend on whether you want to provide for crawlers/clients, and you’d probably have to check documentation for if a particular crawler uses it.