Thank you for your question. Hareem has six meanings: 1. Sacred and forbidden, 2. The cloth worn by pilgrims during Haj, 3. Property, an area belonging to a house, mosque, or institution and not the public 4. Whatever a person safeguards and defends 5. The women belonging to a man 6. The place where a man's wives reside (esp. at the time of the Turkish Muslim sultans who had many wives).
Hareem and Haraam come from the same root [H-R-M], and their meanings are closely related, for this reason I do not recommend it as a name for girls, and Arabs themselves don't use it as a name, especially since when you say "Hareem" their minds immediately think you mean by it "a woman who is a man's property or slave". The English-speaking world also uses the word (spelling it as Harem), and by it they mean "concubines owned by a man". They learned the word and meaning through contact with the Ottoman empire.
Since it doesn't have a positive meaning in Arabic or English, I don't suggest using it.
Tahreem means "to forbid something", to turn someone or something into a "Hareem", for this reason this one too is similar to Hareem and I do not suggest it.
To conclude, Hareem is not a bad name, but the meaning is complex and there are many better names to choose from, for this reason it is best not to use it.