because of latest Google update I want to change my website name from Laura Maroldi to Laura Maroldi Management as well as brand name. Is it possible to shift with with current SEO ranking, backlinks & traffic? Please help.
If you forward the old domain to the new one through 301 Redirect you will save most of traffic, links etc. Registrars normally offer this option in the domain control panel.
Also remember to update your new domain name on Google Webmaster Tools. On Google Analytics you just update Setting with new url, but on Google Webmaster Tools you need to create another site.
Why would you want to change to a longer domain name? Your current one is already too long. And changing will be worst. Don't do it.