You don't have to call it emptiness
It doesn't have to be called “emptiness.” Yes, it's a venerable and traditional term, but what it attempts to communicate is not limited to any one tradition. The main idea is a view and a way of life in which the self, others, and phenomena do not have fixed, rigid, independent essences.
There are many other words for this, such as sūnyatā (Sanskrit), anātman (Sanskrit), anatta (Pali), stong-pa nyid (Tibetan), kōng (Chinese), kū (Japanese), gong-seong (Korean), voidness, paticcasamuppāda (Pali), pratītyasamutpāda (Sanskrit), rten cing 'brel bar 'byung ba (Tibetan), and yuánqǐ (Chinese pinyin).
English-language equivalents include dependent arising, interdependence, dependent origination, conditioned genesis, dependent co-arising, interdependent arising, anti-foundationalism, anti-essentialism, and freedom without foundations.
I find that one of the sweeter, more immediately useful fruits of the emptiness teachings is a kind of freedom of language. There are many ways to say things, and this is a freedom with a wonderful fragrance. Incentives may come up to say one thing rather than another, but these incentives aren't global or universal. They don't fall from the sky. The world just doesn't dictate a “best” or an “only” way to speak. This is a kind of freedom that can be savored joyfully every day!