If your SO died, would you let your future spouse adopt your kids?

In the past year, three of my friends have had their husband adopt their children from previous relationships. In each case, the biological father was crappy and uninvolved. I think a step-parent’s love is really beautiful, because it’s literally choosing to love a child you don’t “have to.”

Anyway, it got me thinking. My SO is a wonderful father, and I know that even if we theoretically split for some reason, he’d always be a great dad. However, if he died unexpectedly and I got married to someone else way down the road who wanted to adopt my daughter, I’m not sure what I’d do. I’d be glad that someone stepped up to fill the father role in her life, but I don’t think I’d want to change her last name, because it’s symbolic of her attachment to her father. What would you do if you were in this situation?

Bonus question - if you died, would you want your SO’s future wife to adopt your child? Obviously it probably wouldn’t involve a name change, but would you be okay with it?