File paths will only be shown if you choose to use folders. If you do, having them displayed in the quick launcher actually helps to identify the nature of the note, and is an additional aid in finding a note not only through the file name, but also through the file path. If you do not want to see paths, just place your notes in the root directory of your vault. You still can use tags for maintaining a hierarchical classification.
Still, the file path will bot be that cluttering if your directory structure is reasonably simple, at most two levels deep. Perhaps you are using a complex folder structure many levels deep? At some point, excessive classification in folders does not anymore help. “Search” rather than folder navigation is the primary tool to locate notes. You may want to consider reducing your folder structure to at most two levels deep.