Strictly speaking, the Code of Canon Law #215 and 216 note:
Can. 215 The Christian faithful are at liberty freely to found and direct associations for purposes of charity or piety or for the promotion of the Christian vocation in the world and to hold meetings for the common pursuit of these purposes.
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.
From observation, this appears to be only enforced in rare instances as “RealCatholicTV”, whose reach in the media and the tone of it’s founder has actually led the diocese where the show is headquartered to make a statement that the group is not authorized to use the term “Catholic.”
Catholic Answers, in contrast, is an approved lay apostolate by its San Diego bishop.
It’s probably OK to use “Catholic” as part of the name in a typical blog–just be sure to differentiate clearly in your posts between your opinion and Church teachings you speak about.