I have sort of a similar situation. That I'll try to explain w/o super confusing anyone
DS's biodad and I were not together. I gave DS a hyphenated my LN-biodad LN, tho, in practical use, he uses DS My LN
I have since married. I hyphenated my LN. Of note, my DH ALSO hyphenated his LN to match. I personally find the hypnenated name a huge PITA, honestly, and it is mostly for solidarity with DH. In common use, I use only my LN most times.
DH's family is not emotionally close, to say the least. He does not feel any strong ties to his family, My father died when I was a child and I am immensely close with my father's family. So, when we had our first "together"- DD, we chose to give her ONLY my LN.
It is nice, bc, even tho DS has a different bio-dad, all of us in the family now have a common name.
The new babies will also have only my LN.
Sure, we get some raised eyebrows sometimes, but we explain that we really wanted to keep the tie to my father's family, and, depending on the audience, we will sometimes discuss how I feel that, as a culture, the practice of the children automatically having the husband's last name is rather antiquated, as we (thankfully) no longer view women and children as property of their husband. Although it certainly is really complicated, I enjoy that we live in a fluid time where surnames are being considered and thoughtfully chosen. (I love some of the thoughts of pp choosing one name to be a family unit.)
OP, I don't know if this is advice or even helpful, but I wanted to share what we had done in a similar situation.