Coconut rice; should it taste like coconut?
When I visited Malaysia and Singapore, the nasi lemak I tried had very little taste of coconut - many of the people I traveled with even got surprised when they heard the rice was cooked in coconut. The name literally means 'fatty rice', which indicates that the coconut milk is added only to make the rice fatty, i.e. more sticky. When I made it myself, the taste actually resembled a less sweet Nordic rice porridge, which you might have had a variant of.  

If you want a more interesting aroma, you could add pandan leaf, if you know where to buy it (probably East Asian groceries). I've heard that bay leaves might give a similar taste, but a single leaf didn't give much of a change when I tried it. Substituting your rice with basmati rice is also an option.