I've heard that the Goths, Vandals and various Germanic tribes were one of the largest bases of Arian Christianity so I assume the shared name isn't coincidence.
Are you perhaps confusing the term with Aryan?
The term 'Arian' and 'Arian Christianity' are because of the association of this version of Christianity with Arius of Alexandria, a presbyter in Egypt in the first half of the 4th century. The popularisation of 'Arian' as an adjective is largely the work of Athanasius, who began using the term to denote his theological opponents (who did have some similarities to Arius' thought, but wholeheartedly disavowed that they were followers of Arius or that this was a correct representation of their theology). Nonetheless, the name stuck.
You're correct in that the Germanic tribes were known as Arian (vs Nicene) Christians. This is because what was considered orthodox Christianity was in flux and depended largely on who was in power and where they were. Valens, the brother of Valentinian I, supported Homoian bishops and theology. He ruled in the East, based primarily at Constantinople. It's during this time that Ulfilas translated the Bible into Gothic and spread it to other Germanic tribes. This particular theological viewpoint was thus transmitted to the Germanic tribes and that's how they ended up espousing this particular type of Christianity.