There's no question that Monty is Addison's biological father, so there really isn't a question of parentage. Monty has been very vocal on his social media accounts of his love for his daughter, sharing photos of her from when she was really young up until now.
Monty has also shared photos from early in his and Sheri's relationship. One of them he captioned with "Sometimes you know. I knew day 1 she was the 1! I love you and miss you! C u soon!"
Clearly, the couple has been going strong since the beginning, and the number of baby pictures Monty shares of Addison confirms that he is almost definitely her biological father.
There is likely more than we know behind the decision of giving Addison Sheri's last name, but as they have never publicly commented, it's not possible to confirm.