Keto diet after transplant?

It is best to ask your surgeon about post operative care as each doctor has their unique regimen. 

Diets never work for the long haul. Here's what does in a nut shell. Calories rule your weight, but it doesn't  matter to count them. Portion sizes are a factor. Don't think in moderation, think in portion sizes. Weigh yourself daily with a scale. Compare day to day's weight everyday. The difference is your wt up or down will tell you if you are eating the correct amount of calories and if your portion sizes are good. Don't diet-consume less calories but don't count them. Use the daily weight comparison of today's weight to yesterday's to gauge your calorie intake. Take care.

  I would not start any dieting changes
immediately post hair transplant.   You
need to maintain good blood flow and nutritional support to your newly
transplanted hair.

you need protein for good quality wound healing and proper take of grafts .. so I think you would better to wait at least 5-6 weeks after HT for starting hard diet .

A long term adjustment to a lower calorie well balanced diet is always going to be the best thing for your hair.  Added exercise is a benefit as well since increased blood flow is very beneficial to your follicles.  I put a lot of patients on the Help Shake whey protein nutritional supplement and they are able to lose weight given the satiety this protein shake provides.  It also has the added benefit of being good for your hair. 

I would wait until you are fully healed before starting any kind of diet. As long as you are getting plenty of protein, eating green leafy vegetables, and taking a hair supplement such as viviscal professional you should be fine and not trigger telogen effluvium. Avoid crash dieting or large amounts of weight loss, it should be a gradual change in order to not affect your hair!

Dieting in your situation seems to be a separate situation for you than the hair transplant you are about to tackle