The name Ibsen is a boy's name of Danish origin meaning "son of Ib". Ibsen and is often added to lists like Cool Baby Names That Start With I and discussed in our forums with posts like "Picky Parents BNG".
From the experts:
Ibsen is a literary hero name possibility, after the great Norwegian dramatist, Henrik I. The name Ib is a short form of Jacob, so you might consider Ibsen as an honorific for or a twin of a Jacob.