Site Title Function

Could someone please tell me the function of the Site Title & Slogan? (not page titles) Normally, my logos have the name of the company within, so it seems redundant to have the logo, then the company name again immediately below (or wherever the site title is placed on the page). Someone was mentioning that search engines look for the site title…is this true? Can the title be used, but simply unchecked to stay hidden? Or does unchecking it disengage it completely?
Thank you for your help!

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