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Neptune, the protagonist of the series, is named after an unreleased console, the SEGA Neptune. The Neptune was meant to be a console version of the 32X add-on and would also be able to play Genesis games. Prototypes of the Neptune were made, but at the same time, the SEGA Saturn was ready for release, and the Neptune never hit store shelves.
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The character MAGES. is named after the parent company of 5pb., also stating that she's related to the party member of the same name from the original and mk2.
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On at least one occasion in each game, Noire states that she and the other CPUs "only do everything", a reference to the PlayStation 3 slogan, "it only does everything".
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Series creator Mizuno Naoko has stated that the core idea behind the series came from two observations:

One was that there were no games on the market that actually dealt with or parodied the game industry itself. The second is that, at the time, characters that changed - that took on different forms - were really popular, but there were none that were cute girls.
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Attachment The character MarvelousAQL is named after the developer of the same name, and her design is based on the five members of the Hanzo Ninja Academy from Marvelous' Senran Kagura series. Specifically, her open shirt and miniskirt are borrowed from Katsuragi, her twin katana and red scarf are borrowed from Asuka, the lining on her boots and shirt are taken from Ikaruga, her red eyes are similar to Yagyu's, and the marks in MarvelousAQL's eyes are similar to the marks in Hibari's eyes.
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The character Tekken is a reference to the Namco fighting game series of the same name. When first introduced in Hyperdimension Neptunia Victory, she mistakenly calls herself "Harada", which is a reference to the creator of Tekken, Katsuhiro Harada.

In the English version, Neptune confuses Tekken's name for "Taken" and thinks she is "That cool actor from that movie where you throat chop everyone to rescue your daughter!" This is a reference to the film Taken starring Liam Neeson.
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In an interview with Dengeki Playstation, the series' development team stated that their ideas for satirical gaming humor came from an "idea box" that any of the staff could add to. The series' fodder enemies, Dogoos, were one such idea presented to the team this way.
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According to series director Shingo Onodera and character designer Tsunako, Hyperdimension Neptunia's initial concept was a fantasy JRPG that involved three princesses and a main character, reworked into Neptune (the protagonist) and the three other CPUs.
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Attachment While Dogoo are an obvious reference to Slimes from Dragon Quest and the Giant Dogoo are an obvious reference to King Slimes, Red Dogoo have a slightly more interesting possible inspiration.

The Red Slimes, as they were known in Dragon Quest when the series was still being localized as Dragon Warrior, were made orange in Dragon Warrior VI, then renamed She-Slimes in Dragon Quest VIII alongside the franchise's localized name being changed.

This is most likely why Red Dogoo are pink and drop Orange Dogoo Jelly.
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Several of the characters from the series were inspired by characters and concepts from other video game franchises:

• Saori from Hyperdevotion Noire: Goddess Black Heart shares her design inspiration with the recurring enemy Tokemei Sister, as they are both based on the character Shiori Fujisaki from the dating sim Tokimeki Memorial.
• While not exactly similar, Hatsumi Sega from Superdimension Neptune VS Sega Hard Girls shares part of her design inspiration, Hatsune Miku and the Project Diva series, with the character Tsunemi from Hyperdevotion Noire: Goddess Black Heart.
• B-Sha from Megadimension Neptunia VII shares part of her design inspiration with Lady Wac from Hyperdevotion Noire: Goddess Black Heart, who is based on Pac-Man. She also shares some character traits with Generia G from Hyperdevotion Noire: Goddess Black Heart, whose design is based on the game SD Gundam G Generation.
• S-Sha shares part of her character inspiration with Ein Al from Hyperdevotion Noire: Goddess Black Heart, whose design is based on the Final Fantasy series.
• Estelle's design is based on the Dragon Quest series has an attack that references the classic Dragon Quest battle interface.
• The characters K-Sha and Lid have several references to the Metal Gear franchise.
• K-Sha has an attack inspired by the same game series as Moru, Monster Hunter, and shares design inspirations with Vio and Lee-Fi, who were based off Resident Evil and Street Fighter's Chun-Li, respectively.
subdirectory_arrow_right Hyperdimension Neptunia (Game)
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The Four CPU goddesses, and the lands they hail from in Gamindustri, are designed and named after consoles from the video game industry:

Neptune (Purple Heart) / Planeptune - The unreleased Sega Neptune. A two-in-one Sega Mega Drive and Sega 32X hybrid.

Noire (Black Heart) / Lastation - Sony's PlayStation 3. Her name is French for the color black.

Vert (Green Heart) / Leanbox - Microsoft's Xbox 360. Her name is French for the color green.

Blanc (White Heart) / Lowee - Nintendo Wii. Her name is French for the color white.
person DrakeVagabond calendar_month December 4, 2023
Mizuno Naoko interview confirming the console war inspiration and Neptune being based on the Sega Neptune:
https://kotaku.com/hyperdimension-neptunias-creator-dreams-of-a-fighting-g-5947178

General facts article detailing other references:
https://www.thegamer.com/hyperdimension-neptunia-facts/
subdirectory_arrow_right Hyperdimension Neptunia (Game)
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Attachment Compa and IF are named and designed after the game's developer Compile Heart and the publisher Idea Factory respectively. Both characters prominently feature design elements from the logo of their respective company (i.e. Compa's Purse, IF's Buckle).