pasupooto no namae ga tadasii ka kakuninsite oku hou ga ii.

The construction ～ておく (te-form + おく) means “to do something in advance” or “to do something and leave it in that state for later.”

• 確認しておく literally means “check (it) ahead of time” or “make sure to check (it) beforehand.”
• It emphasizes preparing or completing the action before it’s actually needed.

Here, か marks an embedded question (“whether the name is correct”). You’re not asking directly but confirming the fact.

• 名前が正しいか確認する = “confirm whether the name is correct.”
• You can indeed use かどうか:
  
  • 名前が正しいかどうか確認する
  • It’s more explicit, but with simple predicates like 正しい, dropping どう is very common.

方がいい (ほうがいい) is used to give advice or a recommendation.

• ～したほうがいい = “it’s better to do ~” / “you should ~.”
• So 確認しておくほうがいい means “it’s better to check in advance” or “you should make sure to check.”

Both are possible:

• 確認しておく方がいい uses the kanji 方.
• In everyday writing, ほうがいい in hiragana is very common and looks more casual/readable.

Both patterns exist:

1. XがYか確認する (no を)
2. XがYかを確認する (with を)
   Japanese often allows dropping を before a noun clause when it’s clear. Both are grammatically correct, though the version without を is very common in speech and writing.

Japanese often omits the subject when context makes it clear. Here, you’re giving advice to someone (often “you” or “we”). So the implied subject is the listener or speaker-group:

• “(You) should confirm in advance whether the name on your passport is correct.”

Yes. In casual speech, ～ておく often contracts to ～とく. For example:

• パスポートの名前が正しいか確認しとくほうがいい。
  Just be aware this is informal.

Both give advice, but the nuance differs slightly:

• 確認しておくほうがいい focuses on the action as a recommendation/planned step.
• 確認しておいたほうがいい uses the past tense おいた, making the advice feel a bit stronger or more like “you’d be better off having already checked.”
  In most contexts they’re interchangeable for giving advice to check in advance.