Script to find the list of stored procedures in all databases I need to pull out the list of stored procedures which are available in my instance. I used the following T-SQL statement to get the stored procedures in a given database.

select * 
from MyDatabase.information_schema.routines 
where routine_type = 'Procedure'


Is there is any script to obtain the all stored procedures or to check the database name of the stored procedure by using the stored procedure name?
You have to iterate through all databases to do that. If you're adventurous enough, you could use the undocumented stored procedure sp_MSForEachDB, which is buggy and unreliable.

Another possibility is using one of its replacements: Aaron Bertrand's or my humble attempt.

Yet another possibility is using a cursor to loop through all databases:

USE master;

DECLARE @name sysname;
DECLARE @sql nvarchar(max) = '
    SELECT 
        DB_NAME() AS [database_name],
        OBJECT_SCHEMA_NAME(object_id) AS [schema_name],
        name AS [procedure_name]
    FROM sys.procedures
';
DECLARE @theSQL nvarchar(max);

DECLARE @results TABLE (
    [database_name] sysname,
    [schema_name] sysname,
    [procedure_name] sysname
);

DECLARE dbs CURSOR STATIC LOCAL FORWARD_ONLY READ_ONLY 
FOR
SELECT name 
FROM sys.databases;
-- you may want to exclude system databases here
-- WHERE name NOT IN ('master', 'model', 'msdb', 'tempdb', 'distribution')

OPEN dbs;
FETCH NEXT FROM dbs INTO @name;

WHILE @@FETCH_STATUS = 0
BEGIN
    SET @theSQL = 'EXEC ' + QUOTENAME(@name) + '.sys.sp_executesql @sql';

    INSERT @results
    EXEC sys.sp_executesql @theSQL, N'@sql nvarchar(max)', @sql

    FETCH NEXT FROM dbs INTO @name; 
END

CLOSE dbs;
DEALLOCATE dbs;

SELECT *
FROM @results;