How do I create a dynamic variable name in React?

Use [] brackets like this

this.setState({["level" + (selectedItem.Level+1)]: FilteredListFromClick})

Prakash's solution works given an advanced enough EcmaScript version.

An older-style and (IMHO) slightly more readable solution is to build the map outside and pass it in.

const newState = {}
newState["level" + selectedItem.Level+1] = FilteredListFromClick
this.setState(newState)