Anyone can call themselves a yoga teacher. It is not a regulated profession. It is not even clearly defined. Ask a dozen yoga teachers What Is Yoga, and you'll get a dozen answers. Yoga is a huge umbrella encompassing things ranging from movement practice, meditation, breath work, philosophy and more. You can post a sign, offer a class, and if students show up: Congratulations, you are a yoga teacher! There are Yoga Teacher Training Programs that offer certification. But again, anyone can offer a Yoga Teacher Training and certify others as yoga teachers. I knew one fellow who offered a TT by taking folks out for a couple weeks of camping, hiking, and instruction to certify them in his brand. Other TTs involve a year of classes, workshops, apprenticing, and mentoring with a score of different instructors.
Occasionally, legislatures suggest government licensing and regulation of Yoga. No one thinks this is a good idea. So far, Yoga remains a libertarian bastion of freedom, safe from governmental interference.  
Similarly, anyone can call themselves an AcroYoga teacher. It is the responsibility of each student to figure out: Does this teacher offer value for me? And more importantly: Is this class safe for me? In AcroYoga, the stakes are higher. As an acrobatic practice, the risks of injury are higher. As a partner practice, the risks depend not only on your own skill and judgement, but also on anyone you partner with. Beginning students necessarily must rely on their teacher's judgement to learn safely. Unfortunately, beginning students have the least context to judge their teacher's skill.
In the Yoga world, the Yoga Alliance sets stardards for teachers and teacher training programs. Yet, in Yoga Alliance Approved, My Ass: "What no one ever seems to acknowledge or mention is that the YA provides no oversight whatsoever. No one checks to see if anyone is actually doing what they say. Everyone is on the “honor” system. Consequently, the registry amounts to a digital rubber stamp or paid advertising." For more on this, see Yoga Alliance Is Ruining Yoga
Is this better than nothing? I don't know - opinions vary.
In the AcroYoga world, we have nothing. We have many teacher trainings, but what it means to be certified is unclear. Would it be useful to have standards agreed by all the teacher training organizations? No one I've asked thinks that is necessary or helpful. I've had the privilege to learn from excellent AcroYoga teachers who hold no formal certification. Conversely, holding a certification is no promise of excellence. The training programs are not, and can not, be responsible for the behavior of their graduates.
Nonetheless, I think there is a conversation worth having in the AcroYoga world. What do we expect of our teachers? What do we expect of the organizations training new teachers? Your thoughts?
As a starting point, here is a superficial comparision of the AcroYoga teaching certification programs I am currently aware: Comparing AcroYoga Teacher Trainings and some questions I would suggest any student considering investing in a TT should ask: 12 Questions for AcroYoga Teacher Trainings
The AcroYoga Curmudgeon