Você estava quase lá:Basta adicionar o usuário à lista de seleção:
select [Usr],
[1] AS January,
[2] AS February,
[3] AS March,
[4] AS April,
[5] AS May,
[6] AS June,
[7] AS July,
[8] AS August,
[9] AS September,
[10] AS October,
[11] AS November,
[12] AS December
from
(
SELECT MONTH(DateVisit) AS month, [User], [User] as [Usr] FROM UserVisit
) AS t
PIVOT (
COUNT([User])
FOR month IN([1], [2], [3], [4], [5],[6],[7],[8],[9],[10],[11],[12])
) p
