Olive Street was built at the same time as Yew Street which is closeby and both streets would seem to have an association with St Matthew's Church beside them. Olive branches are considered a symbol of peace going back to the Biblical account of the flood. (Genesis 8:11)
https://discovernorthernireland.com/whats-on/st-matthews-shankill-parish-church-ehod-2023-p759321