A modern invented name, likely derived from Tinsley.
Tinsleigh is a contemporary American creation, following the trend of adding the '-leigh' suffix to established surnames or place names. It is most closely related to the English surname Tinsley, which originally referred to a field or meadow belonging to a person named Tynni.
Less common today
Tinsleigh isn't in the latest US Top 1000. It last peaked at #5,335 in 2017.
US births per 5-year period, 1990βpresent (SSA data).