Name and gender are probably the two most important customization options for player characters in games, at least for me. Customizing names is part of what lets me comfortably replay games, and make totally different choices.
I prefer a game that lets me choose a custom name, but I like it best if the game can also offer me a few “out of the box” name suggestions. Sometimes I have an exact idea of what I want to name an MC, and other times I don’t really feel like opening up a name randomizer to come up with something good. So I like having 2-3 “default” names to choose from. For settings that are modern or historical that’s relatively simple, there are lots of resources for writers looking for names from particular cultures, nations or time periods.
Fantasy and science fiction is a little more complex. The farther out you depart from a setting that’s grounded in reality, the more power you as a writer have over using the names you suggest as a form of worldbuilding. Especially if your MC is someone to whom a name is an important status symbol or social identifier, and fantasy especially is all about those things.
Now here’s the actual question: name and gender selection will often appear close together, either at the very beginning or the very end of character creation. In an SFF game, you can use this trick to give the idea of gender-based naming conventions – such as, whether they even exist. In my current ChoiceScript WIP, I went ahead and just gave three made-up name suggestions, without gating them by MC gender. Coming up with several suggestions for either male or female (or nonbinary, if you go that route) is only a little extra work, though, assuming you do want that level of convention.
What about other characters? Occasionally, the player can select (directly or indirectly) the gender of a few of the NPCs. Should each of these characters have a male and female (and potentially nonbinary) version of their name? Should they be cognates of the same name (like Agustin/Agustina in Choice of Romance, the first COG game I played), or just two totally separate names? Not all languages have these conveniently convertible gendered names (although most romance languages do, I think). If the name is dissimilar, does it start to feel like a different character?