What is a word for a philosophy that only focuses on efficacy and what is useful?

This definition of Pragmatism is one answer:

Pragmatism [is a] school of philosophy, dominant in the United States in the first quarter of the 20th century, based on the principle that the usefulness, workability, and practicality of ideas, policies, and proposals are the criteria of their merit.

[Britannica]

Obviously, the common noun has a lot of senses. As does utilitarianism.

There are various articles detailing claimed differences in these philosophies. Reddit has:

Utilitarianism, [on the other hand], is a kind of consequentialism that says we should maximize something like happiness, pleasure, or preference satisfaction.

So Utilitarianism prioritises the best perceived methodology to attain say human happiness, while Pragmatism aims for an even harder-to-define usefulness.

A word which fits your seeking is "instrumentalism." Like so much philosophy defining this term can create spirals of meaning, nevertheless an attempt at a definition would be: truth or falsehood is not important, rather the beneficial effects of an idea in helping us work productively with problems are what matter. Under instrumentalism the age old debate around what is true and what is false is not denied to exist but is bypassed. An instrumentalist knows something might be true or false but does not care, rather they want to know what works or helps in some other aspect of life. Knowledge is a tool (an instrument) to help us work with problems.

Two main proponents of instrumentalism are Pierre Duhem and John Dewey. In the online Stanford Encyclopedia of Philosophy the article for John Dewey states regarding instrumentalism: "knowledge and logic are ways to adapt, survive, and thrive." This statement shows two important things to instrumentalism: the omission of the concept of truth or falsehood (notice those terms are not present in the above quotation) and the active focus on simply surviving, even thriving. Therefore whatever helps us thrive as a species within the difficulties of existence would be considered an instrumental approach to life.

'A philosophy that only focuses on efficacy and what is useful' is far too incomplete as a specification of the content of a philosophical theory to enable anybody to correctly classify the theory. First, the term useful, considered in isolation from any context, is incomplete: when we are told that something is useful, we need to know what it is useful for. If the usefulness that is intended here is the usefulness for increasing something like happiness or preference-satisfaction, then utilitarianism may be the right word, but not otherwise. Similarly, if the efficacy in question is the efficacy in increasing something like happiness or preference-satisfaction, then utilitarianism may be the right word, but not otherwise. Moreover, the use of the term focuses here raises the question as to what kind of focusing is intended and what the context of that focusing is. If the theory is focusing on these things as the criteria of moral rightness/goodness, then utilitarianism may be the right word, but if it focuses on them as, say, the criteria of truth then it isn't (in that case, pragmatism, mentioned in another answer, could possibly be the right word).

It is important to understand that when people classify a particular philosophical theory as a version of utilitarianism or empiricism or pragmatism or phenomenology or existentialism etc., they do not do so on the basis of some quasi-legal reasoning that scrutinises whether the theory fits some authoritative definition. What really guides the application of such a term to a particular theory is the theory's similarity to the paradigms (models) of that kind of theories. Jeremy Bentham's An Introduction to the Principles of Morals and Legislation and J.S. Mill's Utilitarianism are generally regarded as the paradigms of utilitarianism: whatever else utilitarianism is, it is what is found in these writings. Numerous other versions of utilitarianism that have appeared since then are classified as versions of utilitarianism because of their similarity to the theories that can be found in the paradigmatically utilitarian writings. Similarly, what makes one an empiricist is that one philosophises in the tradition of Locke, Berkeley, and Hume, the paradigmatic empiricists.

Because of this, competent use of such a term requires that one have at least some general familiarity with the actual content of the theories that serve as the paradigms of the term. Attempting to use such a term solely on the basis of a one-sentence definition one has found in a dictionary is likely to get one into trouble in a serious debate.