'Our Ti-Arne' was born in 1991 and I've got the first examples of Tiarne in South Australia in 1991 as well, so I suspect it's more that the breeders chose a popular-sounding name for their horse. Also in SA I've got similar names such as Tiarni and Tiarnie occurring from the 1970s.
Here's the quick analysis I posted on Opinions, going up to 1995 (asterisk = in the top 500 that year):
1960 -
Tiana1963 -
Tiana1965 -
Tiana*, Tiani
1967 - Teana
1968 -
Tiana1970 -
Tiana, Tiani
1971 - Tiandra*,
Tian,
Tianna1972 - Tianee
1973 -
Tiana, Tiani
1974 -
Tiana, Tiarni
1975 -
Tiana*
1976 - Tiani, Tiarni
1977 - Tiarnie*
1978 - Tiani, Tiarni
1979 -
Tiana*
1981 -
Tiana, Tiani, Tiarnie,
Tijana1984 -
Tianna1985 -
Tiana*, Tiani
1986 - Teanne,
Tian,
Tiana,
Tianna, Tiannah
1987 - Teearn, Tiane,
Tianna, Tiarnee
1988 - Tiahne, Tianah, Tianie, Tiarni-Rose
1989 -
Tiana*, Tiarna*, Tiahni
1990 -
Tiana*, Teana*, Tiahna, Tiani,
Tianna, Tyana
1991 - Tiarna*,
Tiana*, Tiarne*, Tiahna, Tiahne, Tianne, Tiarn, Tiarnee, Tiarni,
Tijana1992 -
Tiana*, Tiarna*,
Tian,
Tianna, Tiarni
1993 -
Tiana*, Tiarne*, Tiahna*, Teanna*,
Tian, Tiandra, Tiarni,
Tijana, Tiahn
1994 -
Tiana*, Tiarna*, Tiahna*, Tiarne*,
Tijana*,
Tian, Tiarn, Tiahn, Tiahnie, Teearna
1995 -
Tiana*,
Tianna*, Tiahne, Tiahni,
Tian, Tiarna,
Tijana, Tearna, Teeyarnna, Tyana
https://nanowrimo.org/participants/christine-seaforth-finch
http://christineseaforthfinch.blogspot.com/