Yes. Собака -> Собаку The literal translation of the sentence would be "How do they call your dog?" Dog is the direct object, and therefore must be in the Accusative Case.
I think they explain this rule, but basically... Syllabic stress in Russian is important. In this case, the stress is on the -A- (со-БА-ка), and any unstressed O's turn into an A sound, which is why it sounds like "са-ба-ка". Also see... молоко, which sounds more like "малако".
“Dogs” is the plural form in English.
“Dog’s” is the possessive form of the singular, for something belonging to a dog.
The literal translation of the Russian sentence is “how call your dog?”, or in slightly better English, “how do they call your dog?”. (The verb form indicates the subject in Russian but not in English.)
But in more natural English, we would say “what is your dog called?” or “what is your dog’s name?”
Neither of those is a word-for-word or literal translation, so you can’t map one Russian word to one English word there. You have to consider the entire sentence as a whole.