An aminophenyl is any amino derivative of a phenyl radical.
An amino group is more basic than a hydroxy group. The amine on p-aminophenol would be protonated, so it would no longer be nucleophilic. That leaves the hydroxy group as the only nucleophile that could attack the acetic anhydride. The major product is p-aminophenyl acetate.
Acid fuchsine is not a pure compound but a mixture of (many isomers of) sulfonated basic fuchsine. So there isn't a proper chemical formula for this mixture.However the compound 'fuchsine' (sic!) is named:" 4-[(4-Aminophenyl)-(4-imino-1-cyclohexa-2,5-dienylidene)methyl]aniline hydrochloride "it may also be called:" Rosaniline hydrochloride "Its chemical formula is presented in the 'Related links' area just below this answer (cit. wikipedia).