Bridge & other card games/transfers
Following a 1 NT opening, partner bids 2D, I say transfer. Can I then bid 2 NT instead of 2H?
You certainly are allowed to bid 2NT, or anything else you wish, but there is no reason that you should want to do that.
When you open 1NT you describe your hand within a fairly narrow range. Partner has a pretty good idea of what you have. He can then look at his own hand and make an intelligent decision whether to play in a part score, invite to game or play in game or slam. He can also look for suit fits or decide on which suit is best by using Stayman or Transfers. He knows, within a narrow range, what the combined partnership assets are
On the other hand, you have no clue as to what partner has. He could have five hearts to the jack and 1 point or he could have 20 points. If partner has 6 hearts to the jack and nothing else, 2H is your best spot and you will probably have trouble making even that. Playing 2NT would probably not be much fun. Even if you have a maximum and only 2 card heart support, you should not override partner. Partner can invite game in hearts or in no trump if he has the appropriate hand. By the way, if you have a maximum 1NT bid plus 4 card heart support, it is perfectly acceptable to "super accept" by jumping to 3H. Here, though, you are bidding based on your good trump fit which is very valuable.
The only justification I could possibly see for bidding 2NT is if your hand contains a likely source of tricks outside of hearts...a good 5 or 6 card minor suit...and you chose to open iNT. Here, I guess you could make a case for bidding 2NT. However, in the vast majority of cases, you should just bid 2H.