Whenever I see someone with this name...

"It's not a common name, so whenever I see someone with it, I am reminded of her."

I would translate this as:

"No es nombre tipico, entonces cuando aparece alguien con el mismo, me acuerdo de ella."

Correct? not correct? A better (more natural) way to say it?

or perhaps:

"no es nombre tipico, cuando lo veo, me acuerdo de ella"

?

I like this one more. Accent marks are important.

You can also say Tiene un nombre raro (raro sometimes has a negative meaning in Spanish though), y por eso cuando lo oigo me acuerdo de ella,

Instead of raro you can use the fancier but neutral inusitado. You can also say es un nombre que no se oye mucho. I think that's best.

No es un nombre común.
"Típico" is not exactly wrong, it's used a lot in colloquial speech with this meaning, but it's better used for talking about something peculiar or characteristic of a region.

Poli's suggestion of "raro" and "no se oye mucho" are fine alternatives. :)

I think I like the "que no se oye mucho" the best. This seems to flow the most naturally.