Yamato's relation to Oden is more complex than the word "fanboy" conveys.
Right when the nation of Wano fell into darkness. When the hero of Wano was arbitrarily judged and executed. When the retainers of the Kozuki family were hunted and believed killed. When the Heir of the Kozuki Family was seemingly strangled and dangled over the edge of the top floor of Kuri Castle by Kaido as it burned. When anyone capable of challenging Kaido (and Orochi) were defeated. Yamato was inspired by the legendary hour and decided to be the existence to carry on Oden's will. Yamato chose to become Oden in order to see the borders of Wano opened to the world - the final wish expressed by Oden before he was killed.
More than a "fanboy" of Oden, I consider Yamato to be an "agent" of Oden. Yamato has inherited Oden's will and has resolved to see Oden's goal of opening Wano's borders (and assisting the figure the world has been waiting for) done. Just as Luffy is an agent of "Joy Boy". Yamato is an agent of "Oden". Unlike Luffy though, Yamato knows who Oden is and chooses to inherit Oden's will. Luffy has no idea who Joy Boy is but destiny and fate are guiding Luffy as the current eras "Joy Boy". The word "fanboy" is in my opinion too hollow to describe the current feelings Yamato has for Oden. Yamato is honoring Oden by becoming him and seeing his will through.
There is also the mental state that goes along with the events Yamato was exposed to as a young child and the environment they had to grow up in. From the age of eight, Yamato has been imprisoned and abused by his father. Being so young and cast into a world of darkness, it follows that Yamato's mental state and psyche would inevitable be affected. "Oden" and embodying such a magnificent person who laughed in the face of death and defied all odds to become the hero of Wano, such an image may have become a source of strength for someone in Yamato's circumstances. Yamato choosing to be "Oden" could go beyond merely being obsessed by Oden.
Additionally, I also wonder if Yamato is treating "Kozuki Oden" like a mantle. As is common in Western "Superhero" comics, certain characters inherit the mantle of an identity/symbol from a past character that died, retired, moved on, or by other circumstances were unable to continue representing the mantle e.g. the current story of Elektra assuming the mantle of Daredevil with Matt unable to continue as The Man without Fear. Oden was Wano's superhero and Yamato has taken up the mantle and become Oden to finish what Kozuki Oden was not able to complete (opening Wano's borders and assisting "Joy Boy"). Yamato assumed a similar style of clothing as Oden (the "mantle"), and even refers to Oden's journal as their bible (The Bible - where the "take up the mantle" idiom originates from).
Beyond opening the borders of Wano Kuni, Oden also mentions that "the entire world awaits a figure ("Joy Boy")…and when that figure appears after an 800-year span, this country must be prepared to welcome and work with them."
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Yamato twenty years later to Luffy - "…someone else has to carry on Oden's will!! That's why I choose to open this country to the world!! I want to fight on your side!!!"
From a certain angle, Yamato seems poised to continue working with the figure the world has been waiting for beyond Wano, especially when you take into account Yamato inviting himself aboard Luffy's ship.