Who determines the reference rate when LIBOR goes away?

The Alternative Reference Rates Committee (ARRC) is a group of private-market participants convened by the Federal Reserve Board and the New York Fed to help ensure a successful transition from U.S. dollar (USD) LIBOR to a more robust reference rate. The ARRC’s recommended alternative is the Secured Overnight Financing Rate (SOFR). It is important to note that the ARRC makes recommendations that will likely be followed by most lenders; however, the ARRC’s chosen fallback rate is entirely elective for lenders.  Some lenders may choose fallback rates other than SOFR.

Generally speaking, most loan documents give the selection of a fallback index to the lender or loan servicer.