The name Ingmar is a boy's name of Norse origin meaning "son of Ing". Ingmar and is often added to lists like Cool Baby Names That Start With I and discussed in our forums with posts like "Fourth Letter In".
From the experts:
Ingmar is known here almost solely through Swedish director Ingmar Bergman. Ing was the powerful Norse god of fertility and peace, who lent his name to several mortal variations, more notably to English-speakers the female Ingrid.