Lines that pass through the same point, are called "concurrent lines" Lines that are always parallel, are called "parallel lines"

Добрий вечір, Франческо. sheaf/bundle of lines proper sheaf/bundle of lines improper set = assortimento; collezione; raccolta; complesso; insieme (di cose affini); serie; servizio (di piatti, ecc.) Вітання з України!

This isn't an answer, but: 1) In physics, but NOT in mathematics, light rays are straight lines, and group of light rays passing through the same point is called a "pencil." 2) In mathematics, the word "sheaf" (and many other everyday works like "group" and "ring" and "germ") has a specialized technical meaning. It belongs to topology, not geometry. It doesn't apply and shouldn't be used here. For the meaning, which I don't understand, see http://en.wikipedia.org/wiki/Sheaf_(mathematics)

Qui: http://books.google.com.ua/books?id=ESSKAAAAQBAJ&pg=PA246&lpg=PA246&dq=%22bundle+of+lines%22&source=bl&ots=W2_QDzNE5v&sig=gESkoLcjEZj27ekDS62HLxr_46k&hl=uk&sa=X&ei=Op05VNHRCaWBywOj7YLYAw&ved=0CGIQ6AEwDQ#v=onepage&q=%22bundle%20of%20lines%22&f=false Qui: http://scientific_en_ru.academic.ru/15037/bundle_of_lines

I agree with Andi's answer. We use words like "bundle" and "sheaf" for physical things, like a bundle of clothes, or a sheaf of wheat. In mathematics, these words just sound comical.