Two words can be written as Haram.
The word Haram refers to something that's forbidden (Haraam). I haven't seen that used as a name and it doesn't sound good to me since it means forbidden. Masjid e Haram also means The Forbidden Mosque.
However there is also the word Haram that's pronounced as HU(mble)+RU(n)+M(other). This one means "sacred place", "forbidden place" (not just forbidden, but forbidden place), and the area inside Masjid al-Haraam is called The Haram (notice Haraam and Haram are two different words).
The first one (Haraam) should not be used as a name because it has a negative meaning, especially in Arab cultures. The second one is usually used as another word for "wife" in Arabic. When a newspaper says "The haram of the Egyptian president" it is a respectful way of saying the president's wife, since his wife is "sacred and forbidden" to everyone except him.
I looked on the internet and found that there is a female singer whose name is Haram an-Noor (both words create one name), and it means Sanctuary of Light, here the name doesn't sound bad. But by itself it could confuse people.
However if it is a common name in your culture then it is up to you.