I have recently started peritoneal dialysis, and since then I've had my period 2 or 3 times a month, is this normal?

No. Dialysis is enough of a stress to throw your cycles off. You are probably not ovulating so your body doesn't get the normal messages when to bleed and when not to. If this continues, you need to talk to your doctor about it and get it in control.
Menstruation in ESRD. Menstruation changes during kidney failure due to fluctuations in hormones. That alone may be more of a factor than doing pd but since pd involves infusing dianeal into the abdominal cavity it may irritate the lining of the uterus and cause spotting. Depending on age and residual kidney function you may want your fsh lh and estrogen levels checked and an ultrasound of uterus and pap smear. Use bcp.
See below. That is a good sign, as the dialysis removes the accumulated waste called uremia, it is allowing the normal hormonal changes to take place.The frequency is not normal and is related to the fact that the removal of waste is not like your normal kidney effeciency better to get checked out by a gynecologist to make sure there are no other causes.