I would like to have. An eye exam at siriraj hospital. I. Am registered. Recommendation for good. Doctor?? Can I make appointment over the phone?

The hospital is a public facility you do not get to choose a Doctor.

Actually you can make a choice on a payment basis at some government hospitals now (and in fact have been able to do so for several decades at Chula). General exam/test or specific for medical conditions? Expect they have specialists as that is a large hospital. Are you a Thai speaker as expect admin many require.

Yes I can speak Thai nic noy I want to check for glaucoma etc

They will likely want a visual field test in that case to go along with pressure test and exam (have that condition myself) - expect they will have the equipment but do not know anything about doctors or facilities (other than one of the top government hospitals).

Can I make appointment over phone? What department etc siriraj?

The hospital is a public facility you do not get to choose a Doctor.

But you do get the fun of queuing up for several hours with the hoi paloi. Just used a government hospital myself to have my eyes checked. Had to get there at 6.30 am to get in the queue for the doctor who arrived at 8.30. Was there for 5 hours compared to about 30 minutes in a private hospital. On the plus side they were more thorough in their examination compared to the private hospital.

Actually Siriraj has a private wing through which you can choose your doctor and make an appointment. But it will of course cost much more, close to the cost of a private hospital. http://www.siphhospital.com/en/index.html

If going through the public channel then indeed cannot choose doctor and will have very long waits.

Just go to the Eye Clinic.

I find the doctors at public hospitals usually make rounds around 8:30 to 9:30, so don't see the crowds until after 9 or there abouts. I usually show up around 9:30 and thus don't have to spend as much time waiting. The only problem with this strategy is some hospitals may only except so many patients a day and you won't be excepted. I've never had this problem, but I'm retired so if I do I'll go back the next day.