Penn State placed Abashidze on administrative leave in September 2018 after reports of sexual misconduct and harassment on the U.S. Center for SafeSport.
Fellow rising seniors Liam Folkes and Kris Myllari will each wear an "A" as Penn State's alternate captains in 2019-20.
Penn State was swept by a strong Nebraska team over the weekend at Medlar Field at Lubrano Park
"It came down to being able to look myself in the mirror and going after my goals and my dreams that I've wanted since I was 12 years old. That's to be on the highest stage and be surrounded by elite mentality, be at a place where we have a chance to win national championships."
Penn State defeated Youngstown State in a close one on Tuesday night but couldn't carry the momentum into their matchup with Pitt.
Page, who came into the draft as a projected late third rounder, averaged 19.2 points per game in her senior season, which is good for 35th in the nation and second in the Big Ten.