I would like to rent a car in Budapest airport in late September through Hertz. I have heard that Hertz has filed for bankruptcy in May 2020. Am I am still able to rent a car through Hertz?
Hertz has not filed for "Bankruptcy".
Instead what they have filed for is something normally referred to as "Chapter 11", or "Bankruptcy Protection". The details of Chapter 11 aren't really a fit for a Travel site, but in short it allows the company time to negotiate with its creditors with a goal of staying in business and having as little impact on their customers as possible.
Many other companies have used "Chapter 11" at some stage in their history, including most of the major US airlines (e.g., United Airlines was in "Chapter 11" from 2002 to 2006, but continued operating during that entire time. Same for American Airlines from 2011 to 2013).
What's more, given that you're renting outside of the US, Hertz operations in many non-US countries are actually "licensees" where they are not actually run by Hertz itself, but instead a local company pays to use the Hertz brand/booking systems/etc — and this is the case in Hungary. Even if the global Hertz operation was to be shut down (which realistically isn't going to happen), the local operation in Hungary would not directly be impacted by that (although they would potentially be indirectly affected).
So yes, you should have no issues renting your car thought "Hertz" (or more so, the local Hertz licensee) in September.