Suzume

Suzume can be pronounced "sue-zoo-me" or "sue-zoo-may". I personally prefer the latter pronunciation, but to each his own.

For this particular spelling, it MUST be pronounced su.zu.may. "e" is never pronounced like the English E in Pete in Japanese. It's not so common a name in Japan now anyway, so not so much of an issue.

Suzumi has the same meaning. This is how you say it:
Su.Zu.me
It is the exact same for Suzumi.