This is a situation that requires you to move carefully, because the rules around parolees contacting current inmates are strict and the consequences of getting it wrong fall on both of you.
The fact that you are not legally married complicates things further. Facilities give more latitude to spouses than to partners or significant others, and without that legal tie the approval process has less of a foundation to work from.
The right way to approach this is through official channels on both ends. On your side, if you are on parole or supervised release, your first call is to your probation or parole officer. You need their sign-off before any contact happens. Going around them and getting caught is a violation that can send you back inside, and that outcome helps nobody including your wife.
On her end, she would need to request correspondence approval through her counselor or submit a request to the warden. The facility will review whether contact between a current inmate and a recently released offender is appropriate given the circumstances of both cases.
It may get approved. It may not. That depends on the nature of both convictions, your conduct since release, and how the facility weighs the relationship. What is certain is that trying to work around the system by using a different name or obscuring who you are creates a much bigger problem if it gets discovered. The risk to her programming, her release date, and your own supervision status is not worth it.
Go through the proper channels and let the answer come back officially.