番号 and 番: identification numbers and turns
Distinguish an identifying number from 番 used for turns or numbered positions.
A number identifying something
番号 is read ばんごう and refers to an identifying number for a phone, registration, room, or similar item. 「予約番号を教えてください」 asks for the reservation number.
「番号を間違えました」 says that the speaker made a mistake with a number, such as entering or recalling it incorrectly. It does not say that the number changed; context identifies the mistake.
Turns and numbered positions
番 is read ばん and means 'turn' in 「私の番です」, or 'It is my turn.' It can refer to a turn without an accompanying numeral.
「三番の窓口へどうぞ」 directs someone to window number three. 三番 identifies the window; it does not count three people waiting.
A number is not necessarily a turn
「番号は十番ですが、まだ私の番ではありません」 says that the speaker's number is ten but it is not their turn yet. It separates the assigned number from the current service order.
「電話番号」 is the standard expression for a telephone number. The use of 番 in numbered labels does not allow every 番号 to be shortened to 番.
Does 「次はあなたの番です」 mean that the person's assigned number will change?
Show the answer and why
No. It means that the other person's turn is next. A change in the identifying number would be stated separately, as in 「番号が変わります」.