What I do for situations like that (I would assume the short term goal would be to start showing up for that brand when you search for it) - I'd decide if it's really possible to get on that search term quickly. For the example "Crazy Man" I would deem it to be a longer term project since it's very general and even a kid will type that in. I would go for the "no-space" version for this one
For a brand term like "Cheese Media" I would definitely start with the space since nobody really searches for something like that and you'd easily get that "brand"
Either way, during the course of your brand name building process (unlinked mentions, links, citations) - I would throw in the alternate version for a certain % of the time. Long term, you'd see your brand to start ranking for that as well.
Personally i prefer making up unique names when im starting a new business, it makes the branding/seo part easier lol
Hope I helped you out somehow 