The current Latin name for the amaryllis genus is Hippeastrum, from Greek hippeos – ‘rider’ and astron – ‘star’, because of the starlike flowers and that the leaves sort of ‘ride’ the stem.
Earlier amaryllis belonged to the Liliaceae family, but much has happened in botany since the summer in the sixties when I collected and pressed plants (not amaryllis). The Liliaceae family has been sorted out and among several new families there is an Amaryllidaceae family which besides Hippeastrum includes other genera such as Clivia, Galanthus (snowdrops) and Narcissus.
In ancient Greek mythology Amaryllis was a beautiful sheperdess who stabbed herself in the heart to create a beautiful flower; The plant was named first in Chile in 1828 by a German botanist.
For Swedes the name is best know from Carl Michael Bellman’s song no. 31, Fiskafänget: http://runeberg.org/fredsang/131.html
Now I have read some more and found that the plant that was originally named amaryllis is a plant of South African origin: Amaryllis belladonna (kapamaryllis in Swedish).