There is a problem with the nomenclature of enzymes that catalyse more than one reaction because they fall into (at least) two structural types. One can refer to both of them as:
multi-functional enzymes or multi-functional proteins
The latter term is used in a 1976 review of the topic.
However for precision it is necessary to employ terminology that distinguishes between them, especially as the term multi-functional has also been used to indicate the different physiological functions that a single enzyme activity can have (e.g. in this review of cysteine cathepsins).
The more common type — to which the lacZ gene product does not belong — can be considered as fusions of proteins containing separate catalytic activity. Examples include the AROM complex of the shikimate pathway of fungi and protists, and the fatty acid synthase complex of eukaryotes. The Wikipedia entry for fatty acid synthase uses the term:
The term, multi-enzyme complex, is often applied to such proteins (as above) but is also applied to complexes of individual enzymes, and so is not suitable as an unambigous descriptor for this type of enzyme.
In the case of the product of the lacZ gene there is a single catalytic site, with a single binding site for the substrate but an additional site to which the glucose produced by hydrolysis of the β-galactoside may or may not bind to produce allolactose. The authors of the linked paper describe this as:
an enzyme with bifunctional activity
This is a description, rather than a ‘snappy’ term, and even so requires further elaboration to remove all ambiguity:
an enzyme with a catalytic site possessing bifunctional activity
But this class of enzyme is relatively rare, which is why I suppose no ‘snappy’ term has (to my knowledge) arisen.