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There's definitely something up with changing from last name to 1st name, but it's not necessarily about being rude. It's usually about being closer.
in Japan people generally don’t call one-another by their first name. Doing so can be a mark of disrespect, unless you’re very close to the other person
Right so, if you're around the same age and have no prior established relationship then usually you don't use 1st name when you 1st meet the person. In such case, using 1st name would be rude. Here, they're not meeting for the 1st time. And in the specific case of Nino and 'Kintarou' (I'm just going to say 'Kintarou' without quotes to mean 'Fuutarou under the disguise of imaginary relative "Kintarou"') using 1st name would imply they've gotten closer/friendlier or that Kintarou is more comfortable with Nino or something.
Also notes:
Note 1.1. Kintarou to Nino: Kintarou, unlike Fuutarou, hasn't exactly met any of the quints, so Kintarou doesn't quite have a reason like 'I would call you by last name, but since you're siblings, I guess I'll have to use 1st name'
Note 1.1.1. I don't think Kintarou has even addressed Nino by any name prior to this scene, at least in the anime. (Coincidentally, I don't think Nino has addressed Fuutarou by any name prior to this episode, at least in the anime, except in the 1st opening. I think Nino usually just addresses Fuutarou as 'anta'/'anata' and even refers to Fuutarou as just aitsu/soitsu/koitsu. The 1st time I think is just in this episode where Nino calls Fuutarou and says 'Moshi moshi Uesugi?')
Note 1.2. Nino to Kintarou: I don't think it's told what Kintarou's last name is clamed to be, but it's probably Uesugi i.e. Kintarou and Fuutarou are paternal relatives, probably 1st cousins. So, I don't think Nino would address Kintarou as Uesugi-kun (and a fortiori Uesugi-san).
Note 1.3. Kintarou to Nino again: In particular, notice that Kintarou doesn't use a honorific eg Nino-san:
In high school, among boys groups, they never use san and kun each other since they can talk casually. (...) But when they talk with girl students, they use san. ESPECIALLY when they call the girl’s first name, they use san not to be regarded as so intimate with each other.
I'm not sure if it's really expected in Japanese for Kintarou to not use honorific, but if it isn't, then I figure Nino can have the same reaction for an address of either 'Nino-san' or 'Nino' and then the use of 'Nino' instead of 'Nino-san' is a slip-up. This may be part of the bigger slip-up that Fuutarou gives away that Kintarou somehow knows that Nino is good at cooking.
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Re Fuutarou to quints: I suspect Fuutarou would've liked to call them all by last name and without honorifics the way in Kaguya-sama Miyuki Shirogane calls others by last name and without honorifics (Shinomiya, Fujiwara, Ishigami, Iino, etc). (It may or may not relate to Miyuki's lack of keigo or whatever. See here from 3:50 - 4:10.)
For honorifics: They're Fuutarou's tutees and are of the same age, so Fuutarou doesn't really need to call them with honorifics.
For last name: But since they all have the same last name, Fuutarou just goes with 1st name.