Looks to me like Oryou is trolling and wrote down the group name as "Tokugawa" Saemonza, imitating Sanada Yukimura who ended up siding against the Tokugawa at the end of the Sengoku period, being not too pleased... in her head at least.
Nah, I think the joke is that they happened to cross paths with another group with a history girl that just happens to use the name of Saemonza's historic rival. Erwin and Caesar are just watching to see if Saemoza's gonna react (which she thought of doing). Oryou at the end is explaining the joke.
Please come this way to be seated~Saka-motoThe Siege of Osaka will have to wait else-where...Yep!That's the way to be a history girlWhat name did you write down?Restaurant during congestionParty of 4...Ma'am, you're disturbing others!Toku-gawa-sama~WhaAa
Att~!?I'm here to avenge myse~lf,
Tokugawa Ieyasu!!Heh heh heh...That there is also a history girl ze yo...Mannerisms of a History Girl
S
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Please write down your name here
Siege of Osaka:
A series of battles undertaken by the Japanese Tokugawa shogunate against the Toyotomi clan, and ending in that clan's destruction.
Wikipedia:Siege of Osaka
Sakamoto Ryouma:
From the Bakumutsu period, Oryou's nickname comes from his wife, Narasaki Ryō.
Wikipedia:Sakamoto Ryouma
Tokugawa Ieyasu:
Was the founder and first shōgun of the Tokugawa Shogunate of Japan.
Wikipedia:Tokugawa Ieyasu
Sanada Yukimura:
Especially known as the leading general on the defending side of the Siege of Osaka, Saemonza's nickname comes from him.
Wikipedia:Sanada Yukimura