A cause that merits attention, aid, or action due to an inherent goodness of values or intention. The lawyer decided to waive her fees because she felt that the young man's case was a worthy cause.
Workers should or deserve to be paid. The phrase comes from the Bible. You did a fine job in the stables, Edgar. I have some money for you, as the laborer is worthy of his hire.
deserving to be so called; good enough to enjoy a specific designation. There was not an actor worthy of the name in that play. Any art critic worthy of the name would know that painting to be a fake.
Deserving a name or description, as in Any artist worthy of the name can draw better than that. This expression uses worthy of in the sense of "deserving by reason of merit," a usage dating from about 1300.