What do you call christian spiritualism? We all walk in the spirit, and we all search for fruit of the spirit, we all want to be spiritual. What do you call that?
What I am saying is that we need not be fearful of the word "spiritual".
Most people understand that the word spiritual simply means other than physical.
There is a spiritual realm, and there is a physical realm.
However, in the spiritual realm, there is a dark side and a light side.
So, if you say you are spiritual, people want to know which side you are on.
And they may divide the realms differently than you or I. For instance, they may consider New Age religions or even white magic to be on the light side.
But to answer your question, I don't use the term "christian spiritualism".
As to what I do call it, I would call it faith. But that term needs to be defined as well.
Someone may ask, "What faith are you?" They are defining faith as a denomination.
Or they may ask, "Are you a person of faith?" Which is a more general question.
They may want to know whether you are an agnostic or atheist. (or not)