The Irish masculine word tiarna is pronounced TEER-nuh, and
Tierney is pronounced TEER-nee. Whilst there is a superficial resemblance to Tiarne, the connection isn’t borne out in pronunciation (tee-AHN).
I had a look at the data, and Tiarne and a dozen or so other variant spellings of tee-AHN, tee-AHN-uh, and tee-AHN-ee (such as Tiani, Tiarna, Tiahn, Teana, and even one Teeyarnna) follow neatly behind the trajectory of
Tiana. The popularity of
Tiana seems to be linked to that of
Tia, as well.
It would seem really unlikely that a girls’ name which sounds nearly identical to another popular girls’ name would instead be derived from an obscure (in Australia) masculine Irish word which doesn’t sound much like it.
It’s also worth noting that whilst the surname
Tierney does show up as a rare girls’ name in Australia it seems to follow the general popularity of /tee/ names for girls, rather than leading.
https://nanowrimo.org/participants/christine-seaforth-finch
http://christineseaforthfinch.blogspot.com/