Below Query shall return the mappings for the requested DbName

SELECT 'DbName', dbPri.name, dbPri1.name
FROM [DbName].sys.database_principals dbPri 
JOIN [DbName].sys.database_role_members dbRoleMem ON dbRoleMem.member_principal_id = 
dbPri.principal_id
JOIN [DbName].sys.database_principals dbPri1  ON dbPri1.principal_id = 
dbRoleMem.role_principal_id
WHERE dbPri.name != 'dbo'

Below Query shall return the mappings for the requested DbName

SELECT 'DbName', dbPri.name, dbPri1.name
FROM [DbName].sys.database_principals dbPri 
JOIN [DbName].sys.database_role_members dbRoleMem ON dbRoleMem.member_principal_id = 
dbPri.principal_id
JOIN [DbName].sys.database_principals dbPri1  ON dbPri1.principal_id = 
dbRoleMem.role_principal_id
WHERE dbPri.name != 'dbo'

Improved Query is below

declare @sql varchar(Max)

 set @sql = 'use ? SELECT ''?'', dbPri.name, dbPri1.name
 FROM sys.database_principals dbPri 
 JOIN sys.database_role_members dbRoleMem ON 
 dbRoleMem.member_principal_id = 
 dbPri.principal_id
 JOIN sys.database_principals dbPri1  ON dbPri1.principal_id = 
 dbRoleMem.role_principal_id
 WHERE dbPri.name != ''dbo'''

 EXEC sp_MSforeachdb @sql