I don’t think the first is really possible without doing some psychological damage to yourself, unless it’s a romantic relationship (but not a marriage of 25 years).

My mom died ~20 years ago, when I was about 12. Even if I’d tried the first, there would have been a mother shaped hole in my life, which is its own kind of pain. She and my dad had been together for nearly 40 years, over two thirds of their lives- how could he forget that? How could he live with himself for doing her the disrespect of forgetting her (from his perspective, and now that I’m an adult mine also, but this might not be universal, and hey, the dead don’t get insulted)? He kept their hyphenated last name until he remarried, and now my stepmom knows funny stories about my mom, she knows her birthday and death day, and she has been welcomed by my mother’s family.

I believe that we as people are mostly formed by those around us. Even when they die, we do carry them with us- I have my mother’s handwriting, taste in tea, and laugh. My father will never be able to say grocery store, because she always called it a grok shop to be cute. Hell, she was a teacher and of her three kids, all are married to teachers and two are teachers themselves. We all eat salade niçoise on Christmas Eve because she wanted summery food while pregnant one Christmas Eve and it started an out of season tradition for us.

If you look hard at the people who loved her, you can still see a reflection of who she was (Just from the above qualities, you can get a small impression). Obviously in my opinion my mother was incredibly special, but I think that’s probably true for everyone- it’s just hard to see it when the person is still around.

Loss is painful in both cases. But the second one turns the the initial pain into something positive.

I could never go with the first method. I'd probably feel like I was betraying their memory.