Not neccesarily - I remember reading a story about a magician who had a woman come up to him and describe in detail the full amazing experience of a magician who had performed the Invisible Deck for her. She laughed as she recalled the exact steps, she recalled where she was, who she was with, what her friend was wearing, all the details about the venue and the room - she remembered the card she thought of, and what the magician was wearing - but not the magician's name! She obviously had a great time - but in and of itself that experience didn't translate into remembering the guy's name. The magician was secondary to the magic.
Here's my problem with that: the magic should always be secondary to the magician. Not in some egotistical way, not in the sense of look what I can do, but the magician is the key to making magic powerful.
When we see something magical, but don't remember the magician's name, we have seen, well, something magical.
When we see something magical, and remember the magician's name, we have seen something personal (and hopefully magical as well).
I feel that we should aim for the latter - and in doing so have them remember us.
Another question: How does your answer change if you're a professional magician? Then your name becomes even more important.