Learn Icelandic: Pabbi þakkar honum.

The verb þakka (to thank) is one of the Icelandic verbs that strictly requires its object to be in the dative case. Even though "him" feels like a standard direct object in English, you must use the dative pronoun honum rather than the accusative hann.

If Dad were thanking her, how would the sentence change?

It would become Pabbi þakkar henni. Because the verb þakka forces the receiving person into the dative case, you must use henni (the dative form for "her") instead of the accusative hana.

Where does the -r at the end of þakkar come from?

The dictionary form (infinitive) of the verb is þakka. Because the subject of the sentence is Pabbi (a "he", which is third-person singular), we add an -r to the stem to conjugate it in the present tense, making it þakkar.

Is pabbi the only word for "dad" or "father" in Icelandic?

Pabbi translates directly to "dad" and is the most common, everyday word you will hear. There is also the word faðir, which means "father", but it is mostly used in formal contexts or written text.