To appear suddenly in one's thoughts.
spring to mind
To appear suddenly in one's thoughts, often as an example of something…
come to mind
To appear in one's thoughts.
not leave one's thoughts
To remain in one's mind for a long duration.
on someone's mind
Preoccupying someone; present in someone's thoughts.
on one's mind
In one's thoughts, especially persistently or recurrently.
top of mind
Foremost in one's thoughts; of greatest concern or priority.