How can we get table name from inside trigger?
This might not be the best approach to dealing for your problem, but it will certainly achieve the stated goal.  

ALTER TRIGGER [dbo].[Trg_ProjectCreation] ON  [dbo].[Projects] 
   AFTER INSERT
AS 
BEGIN   
    SET NOCOUNT ON; 
    declare @TableName sysname
    select @tablename = object_schema_name(parent_id) + '.' + object_name(parent_id) 
    from sys.triggers where object_id = @@PROCID

    exec dbo.myProcedure @Tablename 
END
GO


A better option may be to change the way the trigger is created, and putting the name down manually (if it fits your scenario), for e.g.: 

declare @tablename sysname, @sql nvarchar(max)
set @tablename = '[dbo].[myTableName]'
set @sql = 'ALTER TRIGGER [dbo].[Trg_ProjectCreation] ON  ' + @tablename + ' 
   AFTER INSERT
AS 
BEGIN   
    SET NOCOUNT ON; 
    exec dbo.myProcedure ' + @tablename + '
END
GO'
exec sp_executeSQL @sql