When choosing a therapist, I often advise people to contact, and possibly meet, 2 or 3 different therapists before deciding who to work with. A crucial part of successful, healthy counselling is the relationship that develops between the client and the therapist, and you can only really get a feel of whether or not they are the right person for you by meeting them. By having an initial session, you are able to reflect on how you felt with the counsellor, if you felt safe believe you could learn to trust them enough to open up with your issues and be vulnerable.
I have had experience with many clients who have had counselling before seeing me and described how it didn't work as they had chosen the wrong therapist. They might have felt unsafe or misunderstood, or a wealth of other reasons why their first choice was not right for them. It is a brave move to seek counselling and seeing the wrong one for you can create a negative experience which not only stops the work, but may also cause a client to feel counselling is not right for them. Sometimes it can take many years, and a lot of other pain, before someone feels able to have another try. No counsellor is right for everyone and, just as we choose friends by how well we get along, similar can be said for finding the right therapist.
It is also not uncommon for a client to feel an obligation to continue seeing the first counsellor they meet, and might even worry about letting the counsellor down. As a professional, counsellors know that there is no 'one size fits all' option and would not feel offended if you chose to see someone else after meeting them.
At the end of the day, as a client you are looking for the right service for you and you do not need to feel obliged to continue seeing someone who is not quite right for you. Just as you would shop around for other services, it is ok to shop around for the right therapist too. You are potentially going to be talking about some personal issues, some deep routed fears or negative self-beliefs, so it is important you are seeing someone you can develop trust with.
It is your right to choose a counsellor who you can feel safe with, and who you believe will be able to work in a way that suits your needs. You are investing your time and money so you deserve to have the right service. So have a telephone conversation, arrange a meeting or shop around, and know that your first choice does not have to be your only choice.