Two accusatives with 'fragen', 'kosten', 'lehren' and 'nennen'
In German, when a verb has two objects, one of them is usually a person in the dative and the other is a thing in the accusative: Ich gebe dir das Buch, Sie zeigt mir die Stadt. Once you have learned this pattern, it feels safe to put every person into the dative. A small group of verbs breaks that habit. With fragen, kosten, lehren and nennen, the person stays in the accusative, even when a second object follows.
English speakers trip over this for two reasons. English has no visible case on most words, so there is nothing to warn you. The dative-for-people habit is also so strong that Ich frage dir or Das kostet mir can sound right when it is not. The correct forms are Ich frage dich and Das kostet mich.
These verbs take a person in the accusative (mich, dich, ihn, sie, uns, euch) plus a second accusative: the question, the price, the subject taught or the name. In the pattern lists you will see this as jemanden etwas fragen, not jemandem etwas fragen.
A simple test helps. Before you use the verb with a second object, ask yourself how it works on its own. You say Ich frage ihn (I ask him), not ihm. The person keeps that same case when you add the second object: Ich frage ihn etwas.
A bonus clue is the passive. With these verbs the person becomes the subject: Ich wurde gefragt (I was asked). With a true dative verb such as helfen, that is impossible, and you get Mir wurde geholfen instead.
fragen is the verb you will use most. The person you ask is accusative, and so is the thing you ask about, which is usually etwas, das or nichts. With a real topic, German often uses nach instead, but the person stays accusative. The related verb abfragen (to quiz, to test someone on something) works the same way: Sie fragt mich die Vokabeln ab.
kosten takes the person who pays and the amount of money, time or effort, both in the accusative. The person is often left out (Das kostet zehn Euro), but when it is there, it is accusative.
lehren sounds more formal than its everyday equivalent beibringen. It appears in writing, at school and university, and in sayings about life and experience.
nennen in the sense of calling someone something is slightly different: the second accusative is not a separate object but a name or label for the person. Both parts are still accusative, which you can see in einen Feigling.
The classic mistake is Ich frage ihm or Kann ich Ihnen etwas fragen?. Say Ich frage ihn and Kann ich Sie etwas fragen?. In the same way, Das kostet mir zu viel is heard in some regions but counts as nonstandard. Stick with Das kostet mich zu viel.
Be careful with the synonyms, because they do not share the quirk. beibringen means the same as lehren but takes a normal dative person. You may also hear jemandem etwas lehren in everyday speech. It is common, but the accusative is the safe standard form.
nennen also has a second meaning: to name or mention something to someone, for example a price, a reason or a doctor. In that meaning, the person is dative. The meaning decides the case.
Most German verbs with two objects put the person in the dative, but fragen, kosten, lehren and nennen (to call someone something) keep the person in the accusative: Ich frage dich etwas, Das kostet mich Zeit, Er lehrt uns Deutsch, Sie nennt ihn Max. If the verb takes mich or dich on its own, it keeps that accusative when a second object is added. Watch out for beibringen and for nennen meaning to tell someone something, which take a dative person.