We chose the name (for) the baby. It marked me wrong for this. Using (for) in this sentence makes it more personable.
Some verbs conjugated for "nós" are the same for both present and past and you get them by the context: nós escolhemos = we choose/chose, nós comemos = we eat/ate. Nós lemos = we read/read(past).
baby's = of the baby, belonging to the baby (possessive)
babies = more than one baby (plural)
No, in English you must use the possessive, marked with 's, to show the relationship of baby and name. You might also say "We choose the name of the baby." but it sounds clumsy; the possessive with persons is more natural. Another alternative is "We choose the name for the baby;" (making "the baby" dative/indirect object).
BABY in your last sentence is not an indirect object; it is the object of the preposition FOR.
I was raised with spanish and english and Its still tricky for me. But do you have to do it with english?
This does not have to be past. It could carry the meaning of emphasizing who is choosing the name; ie. WE not YOU or HIM or HER, etc.
Once again, present continuous is more common in English: "We are choosing" is seen as wrong. It should be right, shouldn't it?