If you are between jobs, part-time, temporary, consulting gigs are great. They bring in some money; they keep your brain engaged; they fill this gap in your resume; they usually give you some opportunities to meet or get to know people better; and they can lead to full-time ‘permanent’ work. Here’s my advice: get an LLC. They are easy to set up – most state’s Secretary of State’s Corporation’s websites will give you all the forms and instructions you need. An attorney can help if you want.
Once you have an LLC, you will have clients and you’ll want to refer to it on your resume. There are actually lots of single person LLC consultants. What distinguishes one from the other is clients. I think you are better off describing each client, and then the work you did for them. In the past I’ve used this:
Sample Clients: Japanese Innovative Technology Manufacturer; German Plastic Blow Molding Manufacturer; German Instrument & Controls Supplier; International Developer of Infrastructure Projects; Renewable Energy Project Developer; Top 10 U.S. Bank; French Lending Institution; Global Infrastructure Firm
Then I described the work I wanted to describe (from whichever consulting gig or gigs) that was most applicable to the job to which I was applying.