The name is straight Anglo-Saxon: symbel, "continual, permanent"; myne, "mind, memory."  There are, of course, plants associated with remembrance (e.g. Rosemary, as all readers of Hamlet know) or the appropriately named Forget-me-not.  Tolkien's invented "symbelmynė" or, as he glosses it, "Evermind," would be such a plant in Rohirric culture.  I'm not botanist, but there are flowers which can blossom all year round; and while I don't think that there are any plants which by nature grow near graves, certain flowers have commonly been planted near graves such that the association aries.  The best example which would have occurred to Tolkien: the poppies that were planted in the cemeteries for the fallen in Flanders after the Great War.

On the poppies in Flanders, since we're on the subject:

In Flanders Fields

In Flanders fields the poppies blow
Between the crosses, row on row
That mark our place; and in the sky
The larks, still bravely singing, fly
Scarce heard amid the guns below.

We are the Dead. Short days ago
We lived, felt dawn, saw sunset glow,
Loved and were loved, and now we lie
In Flanders fields.

Take up our quarrel with the foe:
To you from failing hands we throw
The torch; be yours to hold it high.
If ye break faith with us who die
We shall not sleep, though poppies grow
In Flanders fields.

John McCrae (1872-1918); of pneumonia while on active duty.

__________________________________

All that is gold does not glitter,
Not all those who wander are lost;
The old that is strong does not wither,
Deep roots are not reached by the frost.
From the ashes a fire shall be woken,
A light from the shadows shall spring;
Renewed shall be blade that was broken,
The crownless again shall be king.