The reason for this is simple: a big consultancy has an established brand. Clients know the brand and trust it and have a broad idea of what they can expect when working with "someone from that company". This is not the same with a startup consultancy where there is no "company" brand established yet.
Professional services, more than any other business, is all about trust. Clients need to believe that you can deliver and that you have their best interests at heart. This is especially true since the "product" is an intangible, i.e., a service you provide.
The mistake most consultants make is that they try and hide behind the name of their business as they start out. They quickly ask a graphic designer to "make them look as good as a McKinsey" and then hope the phone will ring. It seldom does.
The thing with professional services is that it is people delivering work through people. The way to get your consulting business off the ground is by primarily promoting yourself as the consultant, not your business as the consultancy. You need to market yourself, not your company. Clients need to first believe in you, then in your business.
There is nowhere to hide when you start your own consulting business.
It is tempting to step out of the corporate world and start "your own corporate". The problem is many think they can simply repeat the same marketing approaches of the big corporate, but this almost always fails.
If you decide to start your own professional services firm, you need to become comfortable with marketing yourself and being the face of the business. This is how these businesses always started. It's why law firms, financial services firms and many consulting companies carry the name of the founder. Mr McKinsey first had to market himself before the company could do the same.
As a consultant starting your own consultancy - are you ready to step into the spotlight?