A gene that shows it's effect on more than one character is

A gene that produces many effects in the phenotype is called as a pleotropic gene.
A polygene is a group of non-allelic genes that together influence a phenotypic trait.
Multifactorial inheritance: The type of hereditary pattern seen when there is more than one genetic factor involved and sometimes, when there are also environmental factors participating in the causation of a condition.
Many common traits are multifactorial. Skin colour, for example, is multifactorially determined. So, is height and so also is intelligence.
Multiple gene is another name for polygene.