ALTER USER [<username>] WITH LOGIN=[<username>]

Is the right approach

You can use the following query in the context of your database to check for orphans:

select
    dp.name [user_name]
    ,dp.type_desc [user_type]
    ,isnull(sp.name,'Orhphaned!') [login_name]
    ,sp.type_desc [login_type]
from   
    sys.database_principals dp
    left join sys.server_principals sp on (dp.sid = sp.sid)
where
    dp.type in ('S','U','G')
    and dp.principal_id >4
order by sp.name

ALTER USER [<username>] WITH LOGIN=[<username>]

Is the right approach.

Otherwise go to:

Security > Logins > (your username) > Properties > User Mapping

and remap that user to the database you want.

You can use the following query in the context of your database to check for orphans:

select
    dp.name [user_name]
    ,dp.type_desc [user_type]
    ,isnull(sp.name,'Orhphaned!') [login_name]
    ,sp.type_desc [login_type]
from   
    sys.database_principals dp
    left join sys.server_principals sp on (dp.sid = sp.sid)
where
    dp.type in ('S','U','G')
    and dp.principal_id >4
order by sp.name