If a project or a software is open source, does that mean that I can copy & edit it and then redistribute under my name?

You cannot launch an open source software as your product. I assume that you are not the one who has developed the software. Open source platforms are usually protected by GPL licensing. That means you can only edit or copy the software and use the same for your own project purposes. You cannot however rebrand or sell the software under your name. I suggest you read the licensing agreement carefully before using any open source software. Only then will you come to know about the dos and don’ts.