I realized my site was SEO optimized but only using the <title> tag and not the <meta name=title content=My Website title> tag.Can I have both, the <title> tag and the <meta name=title content=My Website title> tag displaying the same phrase? Would this impact the SEO? 
Does a meta title tag help rankings when used in addition to a title tag?
seo;meta tags;title
Google maintains a list of all the meta tags that it uses. It lists the <title> tag  (although it notes that it is technically not a meta tag).    It does not list  <meta name=title> tags.Most websites rank very well without meta tags named title.   I've never used such a tag myself before.  Your use of a meta title tag would be ignored by search engines and have no impact on your rankings.You already know that it is very important to use a <title> tag on each page for SEO.  The <title> tag is the place on the page where Google gives the most weight to the keywords you use.