It depends on the type of business conducted by the LLC, as well as the laws/rules of whatever state that LLC is registered in. For changing the name with the IRS (once done/approved at the state level) see https://www.irs.gov/businesses/business-name-change
Basically, at the federal tax level a Partnership and Multi-member LLC are somewhat the same thing. So the requirements for a Partnership as indicated on that website, may apply. Also check out the link to publication 1735 on that web page to help you determine if you need to obtain a new EIN with the name change.
