Why BG level is high in the morning

One possibility - dawn phenomenon:

http://www.diabetes.co.uk/blood-glucose/dawn-phenomenon.html

The other possibility may be low blood sugar during the night that is resulting in a rebound morning highs. Basically, this is the body's natural response to low blood sugar.

Testing BGL every couple of hours over the night time will give an indication as to whether there are lows occurring or not. If you find that there are no low blood sugar events during the night time - then I'd imagine it's more than likely DP which is causing the high morning sugars.

There are many different ways to combat DP, some report that a fat based snack before bed helps. Others opt for a correction dose of QA insulin in the morning. Others who use basal/bolus insulin overlap their basal dosages so peak activity occurs around the time that they wake to combat the effect.

I have no idea what the procedure is for pumps so cannot advise. But I'm sure someone on here will be able to assist. Failing that, your doctor will hopefully keep you right.

I'm surprised that he/she never discussed DP when you mentioned the high reading a between 0200-0800 though...

Good luck,
Grant

As @GrantGam1337 has stated, whilst the result of Dawn Phenomenon and Somogyi (reaction to a hypo upto 24 hours before) are both high blood sugars, the cause of both are different, so the only thing you can really do is work out the cause. If you can do a couple of nights worth of blood tests, to see if there is any kind of pattern, and then you'll know the best resolution. If it is Dawn phenomenon, you generally look at increasing basal on the pump slightly a couple of hours before the rise starts, and if it is somogyi, you need to look at cause of the hypo. This may be lowering the bolus CarbFactor for the previous meal, or lowering the basal before the period when the hypo occurred.
Only once you have a better idea of the cause can a specialist start to advise the best course of action, but I hope this give some food for thought? If you can use CGM or Libre GM (even for a week or two) it will simplify this investigation enormously. Good Luck and let us know if you see a pattern.