I have an iterative process for designing a logo and potentially the brand identity too. If a client has provided all that is required for the project then I'll rephrase that brief and send it to the client just so that it is established that we are on the same page and the scope and deliverables are clear and then I'll start designing stuff, of course, we'll discuss the pricing prior but I didn't mention because it is obvious.
If the brief is unusually brief then I prefer hopping on a call with the client and discuss critical aspects like goals for the logo, target audience, and all that. This process clarity of purpose and help position the brand precisely what the client wants.
Then I go toward the mainstream process of designing like creating style scapes getting feedback and iterating on them and then present the ideas and then the final deliverable.