Will using my middle name affect my SEO?

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I would say add your middle name. I'm not sure what you mean by 'memorable ring' but if it is something unique / catchy then it'll make it easier for people to remember.

As there are already a few results appearing in the SERPs, it will be beneficial for you to add it to make the search string longer and differentiate yourself. Therefore, when people do search for you, after knowing about you through other forms of advertising and promotion, you stand a better chance of appearing higher up the rankings at an early stage of your SEO process.

Once you gain more recognition and your website and SEO progress matures you will stand a good chance of being high up in the rankings for the first and last name combination search too.