The original name was 'Reizenin' (冷然院), and it was renamed 'Reizeiin' (冷泉院) when it was restored around 954, because 'Reizenin' (冷然院) was considered unlucky for the reason that the character of '然' was similar to '燃' which means 'burn'; in fact, it had burned out and been restored a few times.
なお始めの名称は「冷然院」であったが、たびたび火災による焼失と再建を繰り返したことから「然」の字が「燃」に通じ不吉であるとされて、天暦8年（954年）頃の再建の際に「冷泉院」に改称した。