As the image below shows, on my DB I also have 2 columns that appear in the results pane separately - first name and last name - (lower part of image)
How do I join them together in the report builder?
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In SSRS you don't join them in the result set (unless you do it in the data source) but you can use expressions in the design to show them concatenated in your report.
Have a look at Expressions (Report Builder and SSRS).
Your expression would be something like
=Fields!FirstName.Value & Fields!LastName.Value