Should I get certified as a product manager?
There are many product management certifications available from reputable companies that provide valuable training. However, there is little evidence that these certifications are highly valued in general by employers. Having a PM certification is unlikely to make you less attractive as a candidate, but it might not make you significantly more marketable. Aspiring PMs might consider certification to demonstrate that, although they don't have work experience, they have invested time and effort in learning about the discipline.
There are other certifications that are Agile/Scrum related, e.g., product owner certification. These more general certifications may be perceived as more valuable by organizations that are using Agile methodologies (most organizations).
In our experience, participants in product management training like the idea of getting certified to demonstrate they've made the professional development investment. If you check job postings for product management positions, you'll find that few of them refer to certification at all, much less a particular certification.