Bandai Priname
バンダイ プリネーム
Seems to be used in a vending machine found in arcades to make your own business cards (名刺). These ones are blank and were made without inputting a name.
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Source: メルカリ
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Translation note: Name card means business card.
This source states that these machines were in Pokemon Center Osaka during at least 2000-2001.
Edit: Here is an advertisement from the CoroCoro Magazine 1998 September Issue on Pokemon Priname.
Pictures of Priname Machine Manual
Edit: Here is a picture of a manual featuring pictures of the machine:
Here is a picture of the manual, which shows a sketch of the machine.
This post says that these machines could have been found in arcades:
This site says that it first appeared in November of 1996, and that if you received a card saying “Congratulations”, you could exchange it for an album that could hold these business cards.
Here is a picture of the album:
A blog also discusses these being in operation here:
This source likens it to Purikura (プリクラ) machines, which are a similar type of machine in arcades in Japan, which are essentially photobooths.
Non-Pokemon General Priname Information
It seems likely that this is a kids/gamified version of existing business card vending machines (名刺印刷機専) in Japan.
Here is a blog post detailing one person’s experience with more formal business card vending machines: 30枚1000円!新宿駅西口の名刺自動販売機を使ってみた - こまめブログ別館
Here is an image of a more formal business card vending machine that looks similar in appearance to the sketch of the Priname machine:
Finally, it seems that Pokemon was not the only IP to be used for these vending machines.
Here is an image of a sealed Hello Kitty back of name cards belonging to the Priname brand:
Additionally, Priname Petit (プリネーム プチ) seems to be a smaller line of these cards. Both Priname Petit as well as the normally-sized Priname cards seem to have been popular with the IP Horipro Idol Paradise (HiP), with Horipro being a Japanese talent/idol agency.