It looks like you're substituting one surrogate identifier for another. Introducing a surrogate key is sometimes (incorrectly) called normalization, so you may get some hits on that term.
In rare cases, normalization requires the introduction of a surrogate key, but in most cases, it simply decomposes a relation (table) into two or more, in such a way that no information is lost.
Surrogate keys are generally used when a natural or candidate key doesn't exist, isn't convenient, or not supported (e.g. composite keys are often a problem for object-relational mappers). For criteria on picking a good primary key, see: What are the design criteria for primary keys
There's little value in substituting one surrogate identifier for another, so the procedure you demonstrate has no proper name as far as I know, at least in the relational model.
If you mean to introduce a surrogate key as an identifier of a new entity set to which the original attribute is transferred, that's close to what Peter Chen called shifting a value set from the lower conceptual domain to the upper conceptual domain. You can find more information in his paper "The entity-relationship model - A basis for the enterprise view of data".
As for your question's title, it's not wrong to say that you're adding a relationship to a table (though that wording mixes conceptual and physical terms), but note that in the entity-relationship model, a relationship is represented by a two or more entity keys in a table (e.g. (id, example_foreign_key)
in the example table) and not by a foreign key constraint between tables. The association of relationships with foreign key constraints came from the network data model, which is older than both the relational and entity-relationship models.