I'm starting a website, that is meant for a non-English region, using an alphabet that is a bit different than that of English. Current plan is as follows. The website name, and the domain name, will be in the local language (not English); however, domain name will be spelled in the English alphabet, while the website's title will be the same word(s), but spelled properly with accents. E.g.: 'www.litterat.fr' and 'Littérat'.

Does the difference between domain name and website name character use influence the site's SEO? Is it better, SEO-wise, to choose a name that can be spelled the same way in the English alphabet? From my experience, when searching online, invariably, the English alphabet is used, no matter the language, so people will still be searching 'litterat' (without accents and such).