Would someone with lymphoma only have one swollen lymph node in the neck?

Not usually: Is possible but unlikely.

It depends...: The most common cause of cervical lymphadenopathy (enlarged lymph nodes in the neck area), especially at a young age, is infection/inflammation. The diagnosis of lymphoma relies on a constellation of clinical signs and symptoms including unexplained weight loss, fatigue, night sweats, lack of appetite, progressively growing lymph nodes, etc. If highly suspicious, a lymph node biopsy is necessary.