Yes. This name "person" is common in idea to the three divine persons because this name "person" is not given to signify the individual on the part of the nature, but the subsistent reality in that nature.
The subsistent reality in that nature is common in idea to the divine persons: that each of them subsists distinctly from the others in the divine nature.
Although this community is logical and not real, yet it does not follow that in God there is universal or particular, or genus, or species: both because neither in human affairs is the community of person the same as community of genus or species, and because the divine persons have one being (whereas genus and species and every other universal are predicated of many which differ in being).