You and your partner may not feel particularly strongly about this, but depending on where you live, those around you may. They may make some assumptions about you based on this decision or they may not see it as a decision you made but as a symptom of a different route to familyhood. In North America, you would likely see people concluding:
- 3 different last names: the child was born to the mother but fathered by another man, whose last name the child carries and who is involved in the child's life as a father. You are the step father.
- 2 different last names, child has hers: as above but the bio father has been out of the picture since before the child was born
- 2 different last names, child has yours: she is a "career woman" who doesn't put family first
- all 1 last name: "normal"
- child has both parent's names, hyphenated: normal, but in some geographies (eg small towns) might be seen as stuck-up or snobbish, or that you aren't married
- mother and child have hyphenated last names, father has one of those names: normal but again possibly stuck up or snobbish, though in this case it will be assumed you're married
- all three have hyphenated last names: back to just "normal" since it's possible that was the father's name all his life and the wife and child have taken it.
These are pretty sweeping assumptions to make but they do get made. (People judge very quickly and on very tiny things, and don't bother learning the actual truth most times.) You will also find that doors open to people with the same last name as a child, whether it's at the school, hospitals, etc. Further, if you have another child it's useful for the children to have the same last name.
I know some couples who have chosen a new last name for themselves and their children, and while their own parents may not have been happy about it, it certainly made them feel empowered and at the same time simplified dealing with the rest of their day to day existence.