Hosta 'Blue Giant' is an outdated or incorrect name for H. 'Elegans'.

This is one of the many confusing situations that occur because of conflicting names in hostas. According to The Hostapedia by Mark Zilis (2009), "The name "Blue Giant" was used as a trade name for H. 'Elegans', i.e., as Hosta BLUE GIANT in the 1980s...The name was mistakenly included on the IAC list of non-registered cultivar..."

Schmid includes this as a selection of H. 'Sieboldiana' originated by Henry Payne of Piedmont Gardens nursery in Connecticut.