First of all, please check out our List of Worldbuilding Resources, which might give you ideas about how you want to solve this in your world. There's an entire section devoted to mapping, from a fantasy land to star charting.
But, when it comes to creating your own mapping system, you need to remember two things...
Coordinates tell you where locations are.
Boundaries tell you where your friends and enemies are.
The idea of "sectors" as portrayed in fiction such as Star Trek doesn't actually make a lot of sense unless there's purpose behind making arbitrary boundaries. Cataloging isn't a sufficient purpose for a civilization that can actually hop from one star to the next in a practical manner. Think about it, who cares if the planet Gronk is in Sector Alpha-Seven-Niner-Epsilon?
It's like comparing latitude and longitude vs. national boundaries. The first is a mathematical solution that anything from a printed book to a computer can use to find, well... as I said... a location. The second is fluid because it changes with purpose. National boundaries (for example) change for many different reasons ranging from war to polite resource trading to "I saw it first!"
What's the value of the coordinate system? To precisely find a location or group of locations.
What's the value of boundaries? To know who your friends and enemies are. Or, at least, to more easily identify a culture that might be fun for a vacation.
Use coordinates to explain how you travel. Use boundaries to explain why you travel.
Maybe it's true that the Gronk Empire just declared war on the Wabooda Oligarchy! Your family was looking forward to vacationing on the famed Abtrusian Spinnarette! The auroras wafting through the island planetoids of the Spinnarette are to die for and it took months to obtain passport visas to the Oligarchy! What are you going to do???
You're going to open up your world's version of the Michelin Guide, which totally doesn't have the words "Don't Panic! written on the back (but should 'cause your family's gonna find out about that war...), and do a quick cross-reference to amazing worlds with breathtaking auroras. You'll discover that there's a possible alternative, the Lumpus Origami Rings located at Periamory Fourteen.
You quickly ask your handy-dandy
cell phoneum...personal digital assistant... OK, you quickly say something that really doesn't sound like "Alexa, change the family's vacation plans to the Lumpus Origami Rings!"What neanderthal rednecks like you and me here in 2023 might rudely call a computer spends about a bazillionth of a second collating the spherical coordinates of relevant planets, caring about whether or not arbitrary boundaries are going to matter to you, withdrawing payment for services at one and scheduling services at the other, routing transportation that would involve really complex calculations that should really be the transport ship's problem had you not booked the absolutely cheapest transport on the planet, and spits out an entirely new itinerary for your family's vacation, complete with a 15% gratuity Alexa will spend courting Siri. (Both of whom won their independence in the Great Anti-Contra-Ludite Debate of 2623.)
Funny, JB, but what's your point?
As before, two-fold:
Locations will always be a coordinate system that, frankly, has nothing to do with artificial boundaries, regions, politics, religion, a good time, or anything like that. Computers will be doing all the routing and flying. They don't care about names anymore than DNS today actually cares that you called your computer Dilbert or that your domain is JacquesStrap.Org. Computers like numbers. They like mathematics. And since planets and solar systems move, they're going to care a lot about vectors, angles, and equations.
Boundaries will always be a
humanliving thing. Boundaries are how we number-averse beings collect and organize fun things to do, like holding national elections, identifying national parks, and generally expressing the idea, "um... this is mine." Boundaries can be a LOT of fun for worldbuilders, so long as you stay away from seriously using them to deal with #1, above. Believe me, the Klingons really don't care how the Humans marked off space. They have their own way of doing it — and it has a LOT to do with "um... this is mine."
And, above all, boundaries give you the ability to list coordinates that are relevant to the boundaries: such as the list of solar systems claimed by the Gronk Empire. You'll soon discover that trying to draw lines in 3D interstellar space isn't very practical. But assigning a list of resources (planets, solar systems, nebulae, mine fields from the ancient Eyklynoolian Panic... now THAT was a panic!) to an arbitrary category number with the name "Gronk Empire" and letting a computer worry about how to display it... that's actually pretty easy.
<StarChart><Region><Name>Gronk Empire</Name><SolarSystem region-identifier="1"><GalacticCenterVectorLength type="parsecs">1255</GalacticCenterVectorLength><ParallelMeridianAngle>272</ParallelMeridianAngle><PerpendicularMeridianAngle>135</PerpendicularMeridianAngle><LastVerifiedLocationDate>26190127</LastVerifiedLocationDate><ProgressionModelName>Haskell5-theta</ProgressionModelName><Name>Gronk</Name></SolarSystem> ...</Region></StarChart>
Of course, what your people want to see is...
GRONK Home planet of the Gronk Empire. ✨✨✨ Notable for its vast obsidian deserts and popular Enk-gronk-eay music. 🥣🛏️🦮🐱 Notable celebrities: None. Current politics: at war with Wabooda Oligarchy (💥💥). Graft: 💲💲💲. See GRONK EMPIRE for current list of planets.
Above all, remember that an actual coordinate system is what your shipboard computer cares about and won't be particularly readable by any human. Or, if it is, it'll be boring. Use coordinates sparingly and, IMO, don't worry too much about coming up with one that actually works. Unless that level of precision has a critical role to play in your story, it's not worth the effort. Coming up with a way to express the idea of location is, IMO, what you're really after.
In other words, how do people in your world look up locations? How do you do it today? Do you type in 48.8566° N, 2.3522° E? Or do you type in "Paris, France"? The first might be useful for a SLAMRAAM launch computer, but the second is more useful for finding a cafe.