You can use this code for example which will pivot the data:
On MySQL:
SELECT data.name, 
    if(data.row_number=1,date,null) as date1,
    if(data.row_number=2,date,null) as date2,
    if(data.row_number=3,date,null) as date3,
    if(data.row_number=4,date,null) as date4,
    if(data.row_number=5,date,null) as date5
FROM (
    SELECT @row_number:=@row_number+1 AS row_number, name, date 
    FROM yourTable, (SELECT @row_number:=0) AS t
    ORDER BY date 
    ) as data
GROUP BY data.name;
On SQL Server:
-- Generate demo data
CREATE TABLE #yourTable(name nvarchar(20), date date)
INSERT INTO #yourTable(name,date)
VALUES(N'xxx',GETDATE()), (N'xxx', DATEADD(day,-1,GETDATE())), (N'yyy',GETDATE()), (N'yyy', DATEADD(day,1,GETDATE()))
-- this is your part
SELECT pvt.*
FROM (
    SELECT ROW_NUMBER() OVER(PARTITION BY name ORDER BY date) as rn, name, date
    FROM #yourTable
) as data
PIVOT(
    MIN(date)
    FOR rn IN([1],[2],[3],[4],[5],[6])
) as pvt
-- cleanup
DROP TABLE #yourTable
This will be a dynamic pivot which will adapt if your date list will grow:
-- Generate demo data
CREATE TABLE #yourTable(name nvarchar(20), date date)
INSERT INTO #yourTable(name,date)
VALUES(N'xxx',GETDATE()), (N'xxx',DATEADD(day,1,GETDATE())), (N'xxx', DATEADD(day,-1,GETDATE())), (N'yyy',GETDATE()), (N'yyy', DATEADD(day,1,GETDATE()))
DECLARE @sql nvarchar(max), @columnlist nvarchar(max)
SELECT @columnlist = 
        COALESCE(@columnlist + N',['+CONVERT(nvarchar(max),ROW_NUMBER() OVER(ORDER BY date))+']', 
            N'['+CONVERT(nvarchar(max),ROW_NUMBER() OVER(ORDER BY date))+']'
        )
FROM #yourTable
WHERE name = (
    SELECT TOP (1) name
    FROM #yourTable
    GROUP BY name
    ORDER BY COUNT(*) DESC
)
SELECT @columnlist
-- this is your part
SET @sql = N'
SELECT pvt.*
FROM (
    SELECT ROW_NUMBER() OVER(PARTITION BY name ORDER BY date) as rn, name, date
    FROM #yourTable
) as data
PIVOT(
    MIN(date)
    FOR rn IN('+@columnlist+')
) as pvt'
EXEC(@sql)
-- cleanup
DROP TABLE #yourTable