I'm a big believer in when you learn how to beat a character, you need to understand what they're trying to do. Here's a brief synopsis of NoName as a character.

His gameplan, no matter what the individual's playstyle, is to hit you with his slow, tracking rockets. His Hold-Weapon B puts out two of them that do pretty good damage. After a short while, these will speed up and eventually blow up on their own. By the time this happens, he'll usually have generated enough Hyper Meter to throw out the super version which puts out 6 of those same rockets, with reduced damage per rocket. He can then Hold-Weapon B to send two more rockets out for a total of 8 giant, slow hazards on the screen.

It is important that when this happens, you drop whatever you were doing and decide how you're going to deal with this. It is his turn, now. From here, it differs on playstyle. Some NoNames will lay down laser drones through Hold-Weapon A. Some will continue summoning Dash Drones. Some will do a combination of those and try to hit you with the robo fist. All of these are ploys to harry and distract you from the rockets. NoName will be doing camera tricks to hide their position. You must train yourself to keep track of these projectiles even when they're off screen. That'll not only make you better at handling NoName, but a better AoSX player in general.

If he has extra meter, he'll do the regular Hyper lasers that come from satellite wheel things that then launch toward you. The main reason this is used is as an extra way to cut off paths and force you into either a fist or a rocket. The more meter he has, the more difficult your life is going to be.

--- So, now that you have a general idea of what his gameplan is, here's what you can do about it.

Come up with a plan to deal with the rockets!
This is very important. Probably the most important detail in the match. You never want to get hit by all 8 rockets. There's no point in letting this happen. You have a couple options.

1. Focus on destroying them. This is probably the best option. Figure out what your go-to option is going to be for multiple situations, i.e. "They're around me!" "They're between me and him!" "They're behind me!" "NoName's here and they're closing in!" and have the presence of mind to execute.
2. Focus on wasting NoName's time. If some of the rockets pop, you have the option of ignoring the rest until they blow up on their own. This keeps the total time for 8 rockets on screen at once lower, which means less total danger for you. Also, if he can't see the one or two remaining rockets and he thinks they've all gone away, you might trick him into doing a B Super, which manually detonates any rockets on screen, effectively making him waste a meter.

No Name is weak in conventional matchups before he gets meter.
When he doesn't have super rockets out, he's at a disadvantage. Push it. Don't let him set up. Don't let him get the momentum. He's going to be laying drones that count as ballistics that shoot lasers.

Don't feed him meter.
If you can help it, fire your attacks with purpose. Don't let him have free meter by blowing your stuff up or charging foolish lasers. More meter for him means constant super rockets to deal with and other nasty traps.

Understand what his attacks do.
Dash A is good against passive play since it lays down 3 drones that fire laser balls, then fly around the ring.
Hold A is his only conventional laser, fires twice then peaces.
Special A is his safe way to gain meter by throwing a very high durability drill that weapon links into mines. It also counters heavy aggressive play
Special B is the robo fist. It has big startup, but incredible tracking and will pound through most ballistics. You have to shoot him with a laser either on prediction or on reaction.
Dash Super lays down lots of the laser drones. He'll do this if he's looking for combos.
Regular Super does the Wheels that fire lasers, then travel toward you. Keep moving out of the way and don't get trapped.
Punch Super is very good at letting him invincibly knock you back into a potential trap of rockets.

Tidbits
-Sometimes taking a drone hit is worth doing to avoid a punch, or fat missile.
-NoName's gameplan while rockets are on the field is to set you up to get hit and instill a paralyzing fear in you of what can happen when you do get hit. While these are on field, he's very hittable if you can overcome your fright. If you can poke at him while he's taking risks that're covered by the fear of missiles, you can make him bleed out before you get NoNamed.
-Watch his heat, it will likely be high, take advantage of that and punish him with a quick attack or far-reaching laser.
-Remember that the rockets you're dealing with are a super. Whatever you have to do to get rid of them is okay since he had to spend meter on them, too.
-Please please please please please watch your heat. No one should ever get hit by all 8 rockets, but it can happen if you're just starting out in the matchup. If you have high heat and eat them all plus a punch or another super or something, you're going to get one-shot.