Identity is a tricky thing when you are self-employed. The trick is to playfully inhabit the role of a freelance consultant without it becoming your entire identity. You need to believe that you are, in fact, a freelance consultant to win jobs and similarly, others need to think you are committed and available for projects.
Its a tricky balance and there's no easy way to deal with it.
Warning: You will probably feel like a fraud
Feeling "impostor syndrome" is a natural feeling on a journey towards self-employment. Many people get stuck when this feeling arises and take it as proof that they are not good enough to keep going.
The trick is not to try to make this feeling go away but to embrace the feeling and see it as evidence that you are moving towards something that is slightly beyond your current capabilities. Research from Professors Deci and Ryan on motivation has shown that this kind of discomfort, the kind that emerges when you are attempting something that is beyond your current skillset, is an essential part of intrinsic motivation.
However, a word of warning. If the level of discomfort is extreme and giving you a tremendous amount of anxiety, you may be trying to do something that is too far beyond your current capabilities. Try to think about breaking it into smaller pieces or finding a safe space to practice the behavior before doing it with a client. Asking another consultant or a friend in the business world for feedback can be helpful.