If you have a large number of objects in a schema, you can use something like this to generate all the changes automatically (it only does tables and views, so before you run it, you might need to expand it to SPs, UDFs, etc.)
USE SandBox
DECLARE @OldSchema AS varchar(255)
DECLARE @NewSchema AS varchar(255)
DECLARE @newLine AS varchar(2) = CHAR(13) + CHAR(10)
SET @OldSchema="dbo"
SET @NewSchema="StackOverflow"
DECLARE @sql AS varchar(MAX)
SET @sql="CREATE SCHEMA [" + @NewSchema + ']' + @newLine
SELECT @sql = @sql + 'GO' + @newLine
SELECT @sql = @sql + 'ALTER SCHEMA [' + @NewSchema + '] TRANSFER [' + TABLE_SCHEMA + '].[' + TABLE_NAME + ']'
+ @newLine
FROM INFORMATION_SCHEMA.TABLES
WHERE TABLE_SCHEMA = @OldSchema
SET @sql = @sql + 'DROP SCHEMA [' + @OldSchema + ']'
PRINT @sql -- NOTE PRINT HAS AN 8000 byte limit - 8000 varchar/4000 nvarchar - see comments
IF (0=1) EXEC (@sql)