For a good monitoring of generic brands, we recommend you to fine-tune the monitored keywords. Go to Project Settings - Keywords to track.
We know how much of a struggle it is to monitor generic brands. For example, telecommunications corporation Orange, or the technology company Apple. Our own brand is made up of a generic name: Brand Mentions (also referred to as BrandMentions or brand mentions or even BM). Therefore, we know how difficult it is for generic brands to be monitored as we're facing this issue ourselves.
Yet, you can get great results if you're adding the correct settings.
For instance, in our case, we can add Brand Mentions as a case sensitive tracked keyword. Chances are that people would mention our brand, and not the generic words, with a capital letter. This way, we'll get all the mentions for what is most likely our brand, Brand Mentions, and not the common noun, brand mentions.
Also, you can add your brand's acronym (in our case BM). This will increase the chances of getting accurate mentions for your brand, even if it is a generic brand name.