Can I evolve my Unown [V] from the Neo or Diamond & Pearl series into Unown VSTAR?
No, you cannot. Unown [V] is a different card name than Unown V.
Source: TPCi Rules Team (2022-11-10)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH12_66
SWSH12_66
SWSH12_65
SWSH12_65
DP6_79