Surprisingly, the answer is no.
Most people shut their eyes for hypnotherapy.
Most patients find it more effective to shut their eyes.
Especially for people who are first-timers, I highly recommend you begin by letting the eyelids close.

However, some prefer to shut their eyes, then open them while in the trance. Others leave them open, then close and open them during the trance.

An admittedly small number keep them open the whole time, and report good results. It is not unusual for patients to open their eyes after being in a trance,
and feeling like the trance is still with them. It can take quite some time to come out of a trance. And this is a sign of an effective session.

I mainly practice an invitational technique (see Modalities). This means that I give suggestions, rather than directions.

So I generally start with "You may start by closing your eyes, but you may choose to leave them open".

In summary, hypnosis tends to work better with eyes shut. This is especially true for new patients.
However, it is entirely up to you.
If you prefer to open and close them,
and it works for you, please do so.