It has been suggested that this name should be replaced by linear Gibbs energy relation, but at present there is little sign of acceptance of this change.
The area of physical organic chemistry which deals with such relations is commonly referred to as 'Linear Free-Energy Relationships'.
PAC, 1994, 66, 1077
(Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994))
on page 1136
IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8. doi:10.1351/goldbook