Start with the notice and enquiries
The proposed surveyor has often already shown you how they work. Look at the clarity of the notice, drawings and guidance, then see how they respond when you ask a sensible question.
Ask about experience
Find out whether party-wall work is a core part of their practice and whether they regularly deal with the type of work proposed next door.
Ask about approach
Ask how they prepare awards, how they decide what protection is necessary and how they deal with minor issues during the works.
Ask about fees before appointing
Request the hourly rate, likely total, what is included and what may generate additional charges.
Use reputation as evidence, not proof
Reviews, examples of work and a visible track record help you assess the person, but no single indicator replaces judgement.
The most important test is whether this person appears competent, impartial, proportionate and someone you can communicate with.