Possibly a variant of Sayre, meaning a woodworker or sawyer.
Syer is a rare surname-turned-first-name with roots likely tied to the occupational name Sayre. It historically refers to a person who worked with a saw or lived near a marshy area. In modern usage, it is often chosen for its sleek, phonetic appeal and its similarity to names like Sawyer or Cyrus.
US births per 5-year period, 1990–present (SSA data).