Hang in there and be gentle on yourself. There is no one right way to do it. Likely how you'll feel will change as time passes and there will be things that make you sad, but also you'll find ways of healing as well.
I had a missed mc in March/April. Found out at 8 week private scan that baby had stopped developing at 5 weeks. I knew instantly what was happening as I was certain of my dates (I'd gotten an early BFP 5 weeks before, so there was no way I was on 5 weeks pregnant). I was upset at the time and in shock, but I also sort of knew. I just knew something didn't feel right. I have an older daughter so had been pregnant once before and that pregnancy never felt right or real to me, even though very much planned and wanted. A couple more NHS scans later and it was confirmed.
I was upset and I cried at that first scan, but I'm not sure I really cried much after that. My way of coping was to focus on what needed to be done. Everyone deals with things differently. I'm very task oriented. I wanted to get things prepared. I wanted to understand the medical details and to make lists of what needed to be done, what help I needed from my dh, questions I had, etc. That was just my way of coping (it's my way of coping with many things in life, frankly). I waited 6 weeks for a natural mc and when it didn't happen (and I really needed to think about going back to work), I opted to have a d&c. Personally, I think that was the right choice for me (and it's something to consider, I felt very in control and supported and everyone was really lovely).
But I never really mourned that baby. It wasn't a baby for me. It wasn't my baby anyway. I believe things happen for a reason and that baby just wasn't meant to come to me and that's okay. Like you, I never felt the urge to name it or remember it in anyway. I have friends who lost babies around the same time who have felt that way and their babies have names and memorials, etc. But that would have been more traumatising for me, not healing in any way. I wanted to focus on the future and focus on what was next.
The only thing I did do is that maybe about 6 weeks later we were on holiday and at the beach. It was a rocky, pebbly beach and my daughter and I were walking along throwing pebbles in the sea. I picked one up and sat down with it and thought about that pregnancy and really cried. It was one of the only times I was really emotional about it. I held that stone and thought about it all and then when I was ready, I stood up and threw it into the sea and let it all go. I found out about 2 weeks later that I was pregnant again. I would have gotten pregnant pretty much that day or shortly thereafter. I think finally letting go and feeling at peace with everything and healing in my own way helped to make that possible. I'm 35 weeks pregnant now with that baby. I felt like this was my baby from the start. It was just completely different. It's been very healing.
I've actually cried and mourned a bit more for that loss now that I'm pregnant than I did when I was going through it. Not because I'm sad about that baby that never was, but because it's just been part of me accepting that if that never happened, then I wouldn't have this baby. So it's come in waves and it sneaks up on you sometimes. But it's perfectly okay to not feel too upset or not cry loads or want to do certain things to remember your loss. You may find your own ways to grieve later or you may just get on with things and look to the future. Everyone's different and that's totally okay. There's no one right way. Just take care of yourself and go gentle with yourself right now. (flowers]