What one hit wonder group from the 80s was named after Spock’s Vulcan mother from the original Star Trek series?

It was T'Pau (who wasn't Spock's mom, by the by, but the Vulcan Queen) and their one hit was "A Little Bit of Heart and Soul".

Spock's mother was Amanda Grayson, a human schoolteacher from Earth. She was played by Jane Wyatt.
https://intl.startrek.com/database_article/grayson

but I agree that the answer you are looking for is T'Pau.

Named after a character from the Star Trek TV series, the pop-anthem band T'Pau formed in 1986 The group released their debut single, "Heart and Soul," in early 1987 with little fanfare. After the song was used in a Pépe jeans commercial, however, it became a Top Five hit on both sides of the Atlantic. The resulting album, Bridge of Spies (self-titled T'Pau for its American release), shot straight to number one in the UK. Four subsequent singles from the album entered at least the Top 20, though none broke in the U.S. charts. After touring with Bryan Adams and Nik Kershaw, the band added another guitarist, Dean Howard, and recorded their second album, Rage. The LP stalled at number four on the British charts, and its follow-up, The Promise, barely made Top Ten in 1991. After a farewell tour, T'Pau broke up, though lead vocals Carol Decker began a solo career soon after.

https://www.allmusic.com/artist/tpau-mn0000002923/biography

The question is wrong about both Spock's mother and the "one hit wonder" part.
As they were probably Shropshire's main contribution to the world of pop, I feel I have to point out that in their home country they had one #1 hit, two top tens and six further entries in the top 40.
And they were slightly heavier than their commercial hits suggested.