What is the meaning of Radha Soami (Swami)

Radha = Narayani Devi (Shiv Dayal Ji's wife)

Soami (Swami) = Master or Husband

Therefore "Radha Soami" means Radha ka Soami (Swami) i.e. Husband of Radha ji (Narayani Devi) = Shiv Dayal Ji

Hence "Radhasoami means Shiv Dayal ji"

This term was coined by Rai Salig Ram who used to address Naraini Devi (wife of Seth Shiv Dayal Ji) as "Radha Ji". This is how the name "Radha Soami" came in to being.