Alas, others have greedily snatched up the metri- words for their own selfish purposes. Metrication, metrification, metrizing all refer to defining a distance metric for an abstract mathematical space so as not to change the topological properties of the space. This is not always possible, but what can you do?
Metrication also refers to the process by which a country adopts the International System of Units (aka, the metric system) and abandons its traditional units of measure. (Currently, the United States, Liberia, and Myanmar are the only countries refusing to be dragged forward into the 19th century on this issue.)
What you are doing is picking a particular distance measure , and that is called defining a metric. This is a common phrasing in mathematics, pure and applied. For instance, from Notes on Geometry by E Rees
We could now proceed to define a metric on H by....
The procedure is unimportant because it always entails the same thing. You'll have to show that your definition takes any two points you're considering and gives you a non-negative (real) number that is zero when and only when the two points are the same. That number is called the distance, which additionally must be symmetric (i.e., the order of the points doesn't matter, so the distance from Los Angeles to New York is the same as the distance from New York to Los Angeles) and must obey the triangle equality (i.e., intermediate stops cannot decrease the distance, so the distance from Los Angeles to New York is at most the distance from Los Angeles to Denver plus the distance from Denver to New York.)