Systemically, 1♦ is opened on any balanced 18-19 without a 5 card major and could be short, or any unbalanced opening hand with ♦. A 1N rebid would clarify the hand as the 18-19 hand. Partner will stretch to respond opposite a 1♦ opener.
Your choices for a rebid are:
A support X
2♦ (this is either a weak heart raise, a game forcing heart raise, or around 15-18 HCP with 6+ diamonds. It is forcing, with partner supposed to treat it as the weak heart raise until later bidding clarifies the auction)
2N (which systemically shows 16+ HCP and 6+ solid diamonds in an uncontested auction)
3♦ (100% Game forcing, emphasizing ♦)
3N (undefined systemically, logically to play)
4♣ (splinter)
4♦ (swiss raise of hearts)
You could also cue bid 2♠, but typically we have been using that bid to show an 18-19 NT without a spade stopper, so I've left it out of the poll.
If you make a support X, partner's follow-ups would include XYZ.