There are rules about this sort of thing. Specifically, in the Code of Canon Law (Codex Iuris Canonici, or CIC for short), we read that:
Can. 216 Since they participate in the mission of the Church, all the Christian faithful have the right to promote or sustain apostolic action even by their own undertakings, according to their own state and condition. Nevertheless, no undertaking is to claim the name Catholic without the consent of competent ecclesiastical authority.
For example, if I were to start a club for boys, I would not be able to call it “The Catholic Boys’ Club” without the permission of my bishop (it goes without saying that the Pope could also grant this permission). It doesn’t matter whether my parish priest approves; it doesn’t matter whether we meet on Church property; and it doesn’t matter whether we name ourselves after Our Lady or the saints.
The whole of this section of the Code of Canon Law, “The Obligations and Rights of All the Christian Faithful,” actually makes for some pretty interesting reading. Note that “obligations” are listed in the title before “rights”! This is not because we have many obligations and few rights — one need only read this section of the CIC to be disabused of that notion — but because obligations (an Explorer should read “duties”!) are logically prior to rights. There is no right to call one’s organization “Catholic” because there is no corresponding duty to do so. In some circumstances, there may be such a duty — but only the bishop has the authority to judge that.