Gus as a nn for Octavius?

If you came across a boy called [name_u]Gus[/name_u] with the full name [name_m]Octavius[/name_m], would you wonder how they got [name_u]Gus[/name_u] from [name_m]Octavius[/name_m]? Does the -us ending of [name_m]Octavius[/name_m] merit the nickname [name_u]Gus[/name_u]?

My husband brought up this name. He remembered in Disney’s [name_f]Cinderella[/name_f] how [name_f]Cinderella[/name_f] named a mouse “[name_m]Octavius[/name_m], but we’ll call you [name_u]Gus[/name_u] for short”. It’s referring to [name_m]Octavius[/name_m] who became [name_m]Augustus[/name_m] [name_m]Caesar[/name_m].

Are these valid links, or does it feel insubstantial? Would I have to explain it every time we used his full name? Nowhere seems to list [name_u]Gus[/name_u] as a nickname for [name_m]Octavius[/name_m].
I’m not a fan of the other methods of getting to [name_u]Gus[/name_u], so it’s either [name_m]Octavius[/name_m] or simply [name_u]Gus[/name_u].

(If it does work, it would be quite charming alongside my husbands name, [name_m]Maximilian[/name_m], who goes by [name_u]Max[/name_u].)

I think you can say that [name_u]Gus[/name_u] is a pet name, but I wouldn’t try to say that it’s a nickname for [name_m]Octavius[/name_m]. A shared -us ending is not enough. By that same logic you could also use [name_u]Gus[/name_u] as a nickname for [name_m]Maximus[/name_m] or [name_m]Lucius[/name_m] or [name_m]Cassius[/name_m].