I'm a woman but yes, I can understand your 'need' to have someone call you dad, it's pretty much the same 'need' women have about someone calling them mum. God knows why you've got such a savaging here. Life is pretty much like an old fashioned road map. You follow it, do your best not to get into an accident, but there's always going to be road works, diversions, mechanical failures, etc.
I mean, there might be something that you're missing here. Maybe she doesn't want more kids because she can imagine a time in the not too distant future where she's able to stop being mum 24/7 and start giving more to the relationship. She might want that independence of just the two of you. Perhaps she doesn't feel like waiting another 20 years for that and being nearly 60 before she can finally think that she's got to be there for everyone else except herself and yourself.
Example: As it goes, I'm married and they're 'our' children. We were both able to take up motorcycling in our early 50s because our kids were old enough to manage without us if we got into an accident. Horrible way to look at it but there's some stuff you might not do as a mother if you've got a young un.
Also, she could just be waiting for grandchildren and might not really fancy the idea of a 5 year old of her own and a couple of toddlers who call her grandma. No idea. This is definitely what would've happened to me if I'd decided to go for more kids in my mid/late 30s. Plus, you do realise that kid appeal is definitely still there as a grandfather? Despite the fact that my own had 2 step grandparents as the result of divorce, they called the male one grandad. In fact, they saw more of him than they did of their birth grandad and loved him all the more for it.
I think maybe you need to take a step back and realise that your feelings are valid (despite what the hard asses say here) and then consider whether you would find it reasonable to go and have some talking therapy that will help you reframe the issue. It doesn't need to be a case of you always feeling as if something's missing. You can definitely get to place where you realise that you're whole with what you've got.
Finally, just in case you're really worried that somehow you're going to get screwed over, you can always freeze your sperm and get a surrogate if you're still desperate for someone to call you dad / want to keep your options open.