Counting first and last names appearing more than once - stata

Question

I have the following names:
clear
input str25 names
"Trenton Mercer"
"Carissa Moyer"
"Timothy Delgado"
"Kaylynn Payne"
"Harry Patton"
"Charlie Dudley"
"Harry Schmitt"
"Wyatt Hammond"
"Kasen Delgado"
"Katherine Noble"
"Julius Jarvis"
"Harry Carney"
"Wyatt Holden"
"Megan Wilson"
"Priscilla Shaffer"
"Savanah Marshall"
"Harry Delgado"
"Harper Ballard"
"Harry Mcmahon"
"Alejandro Jarvis"
end
How can I identify which first and last names (separately) come up more than once?
I would also like to count how many times these appear.

Answer 1

Pearly's solution (with split as the definitely best choice for the issue) appears reasonable. But there are still some unnecessary contours. For example, generating tag, b1, b2 variables seems not really needed.
And more important, the final output is not thoroughly consistent, with the counting info just in line with seemingly-random order, which is also different from the original one without clear explanation.
Thus, I try to contribute a solution (which must also have defects), just as a way to avoid those issues while still providing the output that you are seeking for.
split names
foreach v in `r(varlist)' {
egen TotalAppear_`v' = total(`v' != ""), by(`v')
egen LastAppear_`v' = max(_n), by(`v')
replace LastAppear_`v' = LastAppear_`v'==_n
list `v' TotalAppear_`v' if LastAppear_`v' == 1 & TotalAppear_`v' >1
}
It should be noted your description leads to assumptions made in my code as well as in Pearly's solution:
Every name has only 2 parts, i.e. first name and last name, so not including any middle name(s).
You just want to compare within each group (each first name among first names, last name among last names), not comparing any one with those from the other group.