I am a big believer in open source's capacity to create tremendous direct alternatives to existing closed source software. That is often enough to open up an immense amount of value on its own.
GNU/Linux catalyzed this whole space by being an open alternative to Unix.
If the project is approached with thoughtfulness and integrity, this idea is fabulous. Whether it means creating compatible APIs, or simply offering an experience which is a compatible alternative from a user experience perspective, it pays to build open alternatives.
In most areas of useful invention it pays to focus on differentiation, but in open source similarity can be the most powerful approach.
However, you must have an eye towards evolving past this philosophy and way of thinking. It is unlikely that simply following the closed source predecessor is the best way to unlock longterm value for your users, much less your investors and stakeholders.
The best things about the open model is all the special stuff you can only provide because you are open. Whether it is transparency, flexibility, or unique value creation of any kind— That is what you need to discover and communicate.
Your community and company will be driven by value creation, and simply values themselves. The best companies succeed by identifying values and principles that help align customers and potential employees (or contributors). For absolute authenticity, the product approach and company values should be as aligned as possible, and alignment is achieved by narrative building.
When thinking about brand, it is important to recognize that it is a concept that applies everywhere. Your brand is as important to your own team as it is to external stakeholders. Your values, and value proposition, are the source of truth, and your brand is how you communicate it.
Build a brand that can grow past your rightfully narrow view of product development in the early days. Some day you will want to expand your offering, and when you do you should have a brand that provides you the flexibility to do so. Start building the brand early and introspect constantly. Does my name, my logo, my pitch, emphasize values and work for me?
"Open source alternative to X" is a great starting point for great technology and companies, but if you are successful you will outlive that pigeonholed identity quickly. Learn to appreciate the power of brand and narrative and take the steps to ensure you are ready to evolve when the time is right.