Technically, yes, they are related, though remotely, because the Uzumaki clan is distantly related to the Senju clan. Naruto's descendancy from the Uzumaki clan and Tsudnade's being the granddaughter of the First Hokage, from the Senju clan, makes them distantly related.
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Yes because Tsunade's grand mother Mito Uzumaki is the great great great grand mother of naruto
because technically she is kined to Naruto because Mito Uzumaki is Tsunade's grandmother
because tsunade sent jiraiya on mission
She has called Tsunade: Tsunade-sama (Lady Tsunade), Hokage-sama, Godaime Hokage-sama (5th Hokage), and Shishou. (master)
=No, but naruto calls her grandma tsunade just to annoy her.=
She becomes the fifth hokage.