His name, being a Kulin Maratha, is Shrimān Rājā Shivājiraje Shāhājiraje Bhonsale. Shivā is not the name of some "local-goddess" like idiots repeatedly repeat, but of Devi Pārvati herself worshipped across India. (Shiva-Shivā is Mahadeva and Pārvati as a pair). As far as...
As far as Sanskrit (Original) variant when all Communal Designations (Shrimān prefix & -Ji, -Rāje suffixes which indicate he is a Kshatriya Maratha) are excluded, his proper name is still: "Shivāji Brushabala" Because 'Shivā' is feminine & needs to be converted, -Ji is a must.