The previous answer gives you the literal meaning of the name.
Ashoka and Devi were both Buddhists and were directly responsible for the spread of Buddhism throughout the Indian subcontinent, and into Afghanistan, Sri Lanka, and Southeast Asia.
Because of their commitment to Buddhism, a more accurate translation of their daughter's name is "friend of the Buddhist community."
Buddhist practitioners are known, collectively, as the "sangha." The sangha is considered one of the "Three Jewels" of Buddhism, along with Buddha and Dharma (the Buddha's teachings). So the name Sanghamitra signals that her parents wished to align their daughter with one of the Three Jewels.