Check below query.
DECLARE @string VARCHAR(100) = '18 - Dhanvantari Hospital-Koldam, Himachal Pradesh'
SELECT SUBSTRING(@string,CHARINDEX('-',@string)+1,CHARINDEX(',',@string)-CHARINDEX('-',@string)-1)
SET @string = '7 - Stabilization Center-Gadarwara, Madhya Pradesh'
SELECT SUBSTRING(@string,CHARINDEX('-',@string)+1,CHARINDEX(',',@string)-CHARINDEX('-',@string)-1)
Output
Dhanvantari Hospital-Koldam
Stabilization Center-Gadarwara