覚える and 忘れる: retain something or forget it
Distinguish putting something into memory with 覚える, losing a memory or forgetting something that needs to be done with 忘れる, and retrieving a memory with 思い出す.
覚える: put something into memory
覚える describes learning something new so that it stays in memory. 毎日、新しい単語を五つ覚えます。 means memorizing five new words every day, and the material being learned takes を.
Use 覚えています for a memory that remains. 初めて会った日のことを覚えています。 says that the person remembers the day of the first meeting. This state differs from 覚えます as a habit or future act of memorizing.
忘れる: lose a memory or fail to remember a task
忘れる applies when known information slips from memory or when someone fails to remember something they needed to do. 約束を忘れてしまいました。 says that the person forgot a promise, and 忘れてしまう can add regret or inconvenience about that result.
傘を電車に忘れました。 means that someone left an umbrella on the train. The forgotten item takes を and the place where it was left takes に. It does not mean merely forgetting information about the umbrella.
思い出す: bring a memory back
思い出す focuses on retrieving something that was not immediately present in the mind. 写真を見て、子どものころを思い出しました。 says that seeing a photograph brought back memories of childhood.
名前は知っていますが、今は思い出せません。 shows that information may still be known even when it cannot be recalled at that moment. Think of 覚える as storing or retaining, 忘れる as losing track, and 思い出す as retrieving.
Quick check: Which expression fits when you know a name but cannot recall it at the moment?
Show the answer and why
名前は知っていますが、今は思い出せません。 is appropriate. The potential negative of 思い出す says that the stored information cannot be retrieved at that moment.