The word “Krishna” means “the all-attractive” current in ISKCON is due to Prabhupada’s commentary on Bhagavata Purana (1.1.1) and (6.4.33) because according to Gaudiya philosophy the Lord is sometimes called gu?a-karma-n?ma because He is named according to His transcendental activities.

Thus, Krishna in this context means “all-attractive”, because “His transcendental qualities make Him very attractive.”Prabhupada bases this on his translation of the Chaitanya Charitamrita, where a mystical “etymology” of k???a is given as

k??ir bh?-v?caka? ?abdo / ?a? ca nirv?ti-v?caka?
“k?? expresses existence (bh?); ?a expresses pleasure (nirv?ti)”

The translation of bh? given by Prabhupada is “attractive existence”.