Many organisations pay for a Google ad for their name, despite the fact that they are at the top of search results. This is crazy! If someone can easily find your charity or social enterprise in the search results, why pay for them to click through to your site?
However, it may be worth placing an ad if you are a charity and have free Google Ads, or if your organisation doesn't come up near the top of the search results.
Or, if you want to raise awareness of a particular product, campaign or service you could use a Google Ad with your organisation name. For example, when I did a search for RSPCA, an ad appeared for RSCPA Pet Insurance, which raised my awareness of this product. Similarly, a search for Oxfam brought up an ad for the Oxfam Unwrapped website.