The option kVariableName => Symbol changes the symbol used for intedeterminates in a polynomial ring created with gaussianRing. These indeterminates, k's by default, are entries in the concentration matrix.
The object kVariableName is a symbol.
The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/GraphicalModels.m2:2803:0.