I run a small startup team and we are about to hire a person who would hopefully take care of testing (writes and executes) and manage our git source code (like a project manager). What do you think would be the best job title to describe this position?
The normal way to handle git is that the developers manage the source code. Not anyone outside the development team. You will have someone responsible for setting up the repository, setting up permissions, making backups etc., but managing the source code is purely the developers' business.
In a very small company, you might have one person responsible for QA (Quality Assurance) and general IT.
"Test engineer" sounds like a good start. It's basicly the default title for someone writing and executing software tests.
If you want it to sound very important you could go for "quality management officer", but that title usually involves making sure that a product meets quality standards set by norms, standards and laws (for example in medical products).
In your case "code quality manager" could be a compromize between the non-technical "quality management officer" and the more technical "test engineer".