What the label actually specifies for vials
The prescribing information does not leave syringe choice to guesswork. Under Dosage and Administration it directs prescribers to instruct patients using Zepbound vials to use a syringe appropriate for dose administration, giving as its example a 1 mL syringe capable of measuring a 0.6 mL dose, and to always use a new syringe and needle for each injection.
The reason the example is a 1 mL syringe is arithmetic rather than preference. Zepbound doses are small volumes, and a syringe whose graduations are too coarse cannot measure them accurately. A syringe marked only in whole or half millilitres cannot reliably deliver 0.6 mL.
The label also lists the four presentations by name and instructs that patients be trained for the specific presentation they receive. That instruction exists because the presentations are not interchangeable in handling, and someone trained on a pen has not been trained on drawing from a vial.
Why a multi-dose vial does not mean a re-used needle
A multi-dose vial holds four weekly doses, which invites the assumption that the syringe is part of the kit and gets re-used. The label closes that door explicitly: a new syringe and needle for each injection.
The vial is multi-dose. The syringe is not. Re-using a needle blunts it, which hurts more and damages tissue, and it carries contamination back into a vial you will be drawing from for another three weeks.
The storage clock is different for each form, and it is not only about needles
People arriving at this question about needles usually have a second one behind it, which is how long the thing lasts once it leaves the fridge. The answer depends on which presentation is in front of you.
A single-dose pen or single-dose vial can be kept unrefrigerated at up to 30°C (86°F) for up to a total of 21 days, and is discarded after that. An unopened multi-dose vial or KwikPen kept at room temperature is discarded after 30 days. Once opened, a multi-dose vial or KwikPen is thrown away after a total of 30 days at room temperature, 30 days after first use, or after four weekly doses — even if medicine is left in it.
That last clause is the one that catches people out. Four doses is a limit in its own right, not a description of what four weeks of use happens to consume.