I remember when I wrote my first ever short story. I took it in to the writer's workshop at my local convention, and I clearly remember the reaction of Dario Ciriello, who said (among other things) that I had way, way too many characters. I believe the number was 25 or so, in a 7500 word story.
The character number problem was the result of always having been a novel writer. I had come into that story already knowing all the characters because they were from a novel I'd already written, and I felt that it would be more accurate to reflect the actual knowledge of the POV character(s) by giving the names of the people they interacted with. This is not the wrong instinct, necessarily, but when you're working with a short story, or when you're working with the very first chapter of a novel, it's not a practical approach. Too many character names will lose your reader very quickly.
I suggest you think about the number of names as a stack of cards, a bit like a Rolodex. Each time you introduce a new person's name, the reader adds a card. If the cardstack gets bigger than what the reader can hold in short-term memory at any given time, the reader will start to lose track. It's worse when you're dealing with a non-real world, because the unfamiliar names you give to elements of the physical or social environment will also require cards. This is a pretty heavy memory load.
So how do you go about easing that memory burden for a reader, in order to keep a short story from getting out of control, or in order to help your reader enter your world more smoothly? Here is a list of suggestions that I often employ in my own work.
1. Name your protagonist.
This isn't always necessary (in first person narratives, the protagonist can often get away with just being "I") but in fact it helps the reader create an unambiguous "card" for your protagonist if you give them a name. So I highly recommend it. I also recommend:
2. Make your protagonist the subject of the sentence within the first paragraph.
Again, this isn't always necessary, but to have the character appear in the position of actor/person who drives the story, right up front, can be incredibly helpful when you're trying to get grounded and stay there.
3. Keep track of the named characters to be introduced in any scene or chapter.
Making a list of the people present in any scene is often a practical approach. If it's looking like one person, easy-peasy. If it's more like 10, you should see red danger lights flashing! If you can keep track of the number of characters that need to be there, then you can more successfully decide how to manage their cards.
4. Try to introduce characters one at a time - or in systematic groupings.
One at a time is, honestly, the easiest way to remember characters. However, if you are doing the one at a time approach for more than two people, it can start to look like a list, and you may want to vary your approach. In For Love, For Power, I introduced my protagonist Tagaret first, and then when he entered the ballroom with his three friends, I did them all at once to get the names out there, and after that started into the action where each of them had a chance to do different things. Here's what it looked like:
[Tagaret] stepped through the doors into the Eminence's grand ballroom, with his three best friends following behind him. (this section says, get ready to hear about three best friends)
All the finest people were here; Announcements brought out a bigger crowd than musical events. Politicians, gentlemen and ladies murmured in anticipation, their jewel-colored suits and gowns glittering in the electric light of the chandeliers. Tagaret led his friends into the right side aisle, feeling the gossip-hungry eyes evaluate his new height, his poise, and his maturity before moving on.
"Fifth row," he said, as the chandeliers dimmed slightly. He handed extra tickets back to Fernar, Gowan, and Reyn. (after priming you to get ready for them, here are the three names in a list)
"Wow," said Fernar. "Right up front — how'd you get such good tickets to an Announcement?" (Character #1 gets his own turn, in the same order he appears in the list)
Tagaret sighed. "They're for the concert, Fernar. My mother's the patron of the concert series."
"Great," said Gowan. "We can look right up at the Speaker of the Cabinet." (Character #2 gets his own turn, in the same order he appears in the list)
Reyn aimed a punch at Gowan's shoulder. "Come on. Tagaret just said, we're here for the music." (Character #3 gets his own turn, in the same order he appears in the list, and aligns himself with Tagaret against the other two)
Placing Reyn and his alignment move as last in the series helps him to stand out from the others in the list. The scene then continues into more interactions where the three friends get to behave differently from one another. Part of what I was trying to do was prime the reader to get ready for a list of three so that he or she wouldn't start hearing one character after another and then wonder if or when it was ever going to end (would there be five friends? seven?). It's a question of trying to keep the information to a manageable bite size.
5. Use titles and relationships, not just names.
You can have a much easier time if you don't have to give everyone actual names. Readers will have a hugely easier time dealing with Mother and Father or Uncle or Bro or Sissy than they will with names, particularly names in an unfamiliar fantasy or science fiction language. Those relationship-based names will become annotations on a single card rather than requiring an extra card for each. You can also use titles like the Speaker of the Cabinet or the Eminence. These are not quite freebies, since they do require the reader to create a model of the government (I suppose you could call this its own type of card) but they are much more easily parseable because they have meaning in and of themselves, relative to a type of government. Names just have to be memorized as-is, so anything you can do to scaffold them meaningfully will be helpful.
6. Try to stay focused on the needs of the scene at hand (one cardstack at a time!).
When I was writing the first chapter of my novel, the first set of names that came up were those belonging to Tagaret's family, and I chose to keep Tagaret in name form and all the others in relationship form (Mother, Father, his brother). Then I moved into the main action of the chapter, which includes Tagaret and his three friends in a very crowed place. There, everyone was described in relation to their appearance or position, and none of them had names except for Tagaret and his friends. The only other names that appeared were caste names, which have to do with societal structure and do require their own cards (which is one if the reasons I wanted to keep other names to a minimum). At a certain point, Tagaret had an opportunity to mention some of his family members in relation to a topic that the boys were talking about. What I found was that if I actually mentioned his brother's name, it seemed to shift the focus of the chapter back on the "family cardstack" that I had established at the beginning, and make it harder to stay with the action of the scene which was focused on the "friends and society" cardstack.
The point here is that we tend to think of things in groups (names, numbers, etc.). Handling a single group and the names within it is easier than switching from one group to another. When I left behind the family cardstack at the front of the chapter, it needed to stay out of the picture until the main action - the one that required the friends and society cardstack - had finished.
I hope you'll find these techniques useful when you're working with complex worlds that require a lot of names and memorization. Again, anything you can do to make your reader's job easier will help them stay with you.
It's something to think about.