Does any one know why Permutational Multivariate Analysis of Variance Using Distance Matrices (PERMANOVA) is also called adonis?
Actually it isn't -- the statistical method is not called adonis.
The authors of the vegan software package for R (http://vegan.r-forge.r-project.org) implemented the statistical procedure you refer to in an R function called
adonis, but that is just a name for the function, not a name for the method. The name does not appear to be in use anywhere in statistics other than the vegan package. Yet the vegan package is quite popular, so you will see the vegan function name will crop up quite often in online discussions of permutation anova.
The package authors are free to call the function anything they like. Their implementation may have differences or additional capabilities compared to previous implementations of permutation anova, so choosing a new name avoids confusion. "adonis" has a nice ring to it. It sounds a bit like "anova" and includes a number of letters from "distance", so why not? Perhaps the authors also enjoy making a reference to Adonis from Greek mythology, a heroic figure associated with youth and beauty.
My guess is that the authors started with function names
anosim for analysis of similarities and
anodis for analysis of dissimilarities. Then they realized they could interchange two letters in
anodis and make a Greek God. Good for them!
You could write to the vegan authors and ask them whether the function name "adonis" has any other significance, but does it matter?