To me, it looks as if the composer on "Rose of Tralee" may be listed as G[LOV]E[R]. Only the G and E, the upper bit of the L and bits of the R are still readable, but only barely.
The names of the putative composers of "The Rose Of Tralee" are Edward Mordaunt Spencer and Charles William Glover. The illegible name on the illustrated label does not look very much like either of those names to me.