Lilypond provides the \cueDuring and \transposedCueDuring commands to add cue notes. However, these commands do neither print any cue instrument name, nor do they allow the cue notes to be in a different clef than the quoting voice.
To be able to add cue instrument names and/or clef changes, as a workaround, you can define your own function that sets instrumentCueName and the clef for the staff. At the end of the cue music (typically R1*2), you'll have to reset them again. This snippet combines these steps into one function:
\namedCueDuring #"vIQuote" #UP #"V.I" #"Sop." { R1*3 } ... for adding instrument names, but no clef change
\cleffedCueDuring #"vIQuote" #UP #"V.I" #"treble" #"Basso" #"bass" { R1*3 } ... for instrument names plus clef change
The example also shows how to modify properties of the displayed cue instrument names: They are generated as InstrumentSwitch objects, which support all different kinds of interfaces, like the font-interface to modify font settings.
The disadvantage of this solution is that you always have to manually give the instrument name and clef of the quoting voice, because otherwise the function is not able to reset these. However, there is currently no way known to me how to set the instrument name and clef for a quoted voice automatically.