The name "Alaiyo" means "one for whom bread is not enough." This really reflects Beneatha wants more out of life than just the sustenance of bread. Beneatha is also looking for her identity. She refuses to be labelled by her ethnicity or background, she wants to be her own person.
This name is quite insulting for Beneatha, as she might not think the way Asagai thinks and doesn't agree. But, in a way, it is also true.
Hope this helped! :)