Learn Hardcore Korean: yaksok siganeul byeongyeonghaedo dwaeyo?

It grants permission: “Is it okay if (I) do V?” Here, 변경해도 돼요? literally means “Even if (I) change it, is it okay (does it become okay)?” So the whole sentence asks for permission to change the appointment time.

Synonyms for giving/asking permission: V-아/어도 괜찮다, V-아/어도 될까요?
Negative prohibition: V-(으)면 안 돼요 (“You must not/can’t V”)

Why is it spelled 돼요, not 되요?

Because 돼요 is the contraction of 되어요 (from 되다 + -어요). Standard Korean contracts it to 돼요.

돼요 = correct and natural
되어요 = correct but stiffer/less common in speech
되요 = incorrect spelling

How polite is …돼요?, and how can I make it softer or more formal?

Casual: …돼? (friends, close age)
Polite-neutral: …돼요? (most everyday situations)
Softer/more deferential: …될까요? (tentative, considerate), …되나요? (asking if it’s possible/allowed as a fact)
Very formal/business: …되겠습니까?, …가능할까요?, …괜찮을까요? Example: 약속 시간을 변경해도 될까요? sounds more considerate than …돼요?

Is 변경하다 natural here, or should I use 바꾸다?

Both mean “to change,” but:

변경하다: more formal/administrative. Common in notices, offices, customer service.
바꾸다: everyday and neutral. Most natural in casual speech. So with friends: 약속 시간 좀 바꿔도 될까? In a business email/call: 약속 시간을 변경해도 될까요?

Why is it 약속 시간을 (object marker -을) and not something else?

변경하다/바꾸다 is a transitive verb, so the thing changed takes -을/를. Here the object is 약속 시간 (“appointment time”), so 약속 시간을 변경하다 is natural.

You could also say 약속을 변경하다 (“change the appointment [time/plan/place]”), which is broader.
In casual speech, the object marker can be dropped: 약속 시간 변경해도 돼요? (more casual/telegraphic)

Should it be 약속의 시간 instead of 약속 시간?

No. In Korean, a noun can modify another noun directly: N + N. 약속 시간 (“appointment time”) is the idiomatic form. 약속의 시간 is grammatical but sounds literary or unusual in everyday speech.

What’s the difference between 약속 and 예약?

약속: an arrangement/promise with a person (meeting a friend, client).
예약: a reservation/booking with a service (restaurant, hospital, hotel). So:
Friend meeting: 약속 시간을 바꿔도 돼요?
Hospital/restaurant: 예약 시간을 변경해도 될까요?

Why 시간 and not 시각?

시간: “time” in general, also used for a scheduled time in everyday speech.
시각: a specific point in time; sounds technical/formal. Both can be correct, but 약속 시간 is far more natural in conversation. 약속 시각 feels formal or written.

What is the 도 doing in 해도?

It’s part of the grammar V-아/어도, which historically means “even if (you do V).” In the permission pattern V-아/어도 되다, the idea is “It becomes/it’s okay even if you do V,” hence “You may/Is it okay to V?” So 도 contributes the concessive “even” in this fixed pattern.

How can I soften the request even more?

Add polite softeners:

혹시 약속 시간을 변경해도 될까요?
약속 시간을 좀/조금 바꿔도 될까요?
죄송하지만 약속 시간을 변경해도 괜찮을까요? These sound more considerate and are common in Korean pragmatics.

Does the sentence imply that I’m the one changing it? Should I add 제가?

By default, yes—the omitted subject is understood as “I/we” from context. To be explicit: 제가 약속 시간을 변경해도 돼요? If it’s a shared plan: 우리 약속 시간을 바꿔도 될까요? If you’re asking permission for the listener to change it: 약속 시간을 바꾸셔도 돼요. (granting permission) or 약속 시간을 바꾸실 수 있을까요? (requesting them to change it).

How do I say “postpone,” “move earlier,” or “reschedule” more specifically?

Postpone/delay: 미루다, 연기하다
- 약속 시간을 좀 미뤄도 될까요?
- 회의를 연기해도 될까요?
Move earlier: 앞당기다, 당기다
- 약속 시간을 앞당겨도 될까요?
Reschedule (general): 다시 잡다, 일정을 조정하다
- 약속을 다시 잡아도 될까요?
- 일정을 조정해도 될까요?

Is the spacing 약속 시간 or 약속시간?

Standard spacing is 약속 시간 (noun + noun). You might see 약속시간 informally, but 약속 시간 follows the official spacing rules.

How do I pronounce 돼요 and 변경해도?

돼요: pronounced [dwae-yo]. Not [doe-yo].
변경해도: [byeon-gyeong-hae-do]. The ㄱ in 변경 links smoothly to 해; there’s no extra syllable inserted.

What’s the negative/forbidding version of this?

Use V-(으)면 안 되다:

약속 시간을 바꾸면 안 돼요? = “Is it not allowed to change the appointment time?” / “We can’t change it, right?”
Statement: 약속 시간을 바꾸면 안 돼요. = “You must not change the appointment time.”