If you obtained an FEIN as a Sole Proprietorship or Partnership and are forming a Corporation you MUST obtain a new FEIN for the new company.
If you are forming an LLC and the number of owners will not be changing (i.e. you obtained your FEIN as a Sole Proprietor and you will be forming a single-member LLC or you obtained your FEIN as a Partnership and will be forming a multiple-member LLC) then you can use you existing FEIN.
However, notifying the IRS of the name change (adding “LLC” to the company name) is more complicated than simply obtaining a new FEIN. In short, it is almost always easier to obtain a new FEIN.