When I registered for Alerts using Text on my cell phone, I created a Nickname, but when I went to the Notifi Preference webpage on the GMP website, the Nickname was not there.

The (text) Nickname you set up on your cell phone is at the “account” level. This helps if your phone is registered to receive alerts from more than one account. For example, “Home”, “MomsHouse”, etc.
The Nickname on the preference webpage is a “contact” Nickname which makes it easier to identify the different phone numbers and emails registered to receive alerts from your account. For example: “Mom’s office email,” “Dad’s Cell.” Each account can have multiple contacts registered to it.