It's not that Game of Thrones is above sexual innuendo — it definitely isn't. But in the case of Petyr Baelish's nickname, its origins aren't as saucy as you would imagine. I could also see him being nicknamed Littlefinger because of some shady business venture gone awry, resulting in someone chopping off a part of his finger, and the nickname sticking. But that isn't it either. So why is Petyr Baelish called Littlefinger on Game of Thrones? The nickname actually comes from his beloved Catelyn Stark's brother, Edmure, who grew up with Baelish after Lord Tully took him in as his ward.
There is a region of the rocky peninsulas near the Vale of Arryn called The Fingers and Petyr Baelish's father was lord of the smallest one. Baelish was just a boy when he inherited it, and he was slight for his age, so he earned the nickname "Littlefinger" as a kid and it just stuck. According to a passage in the books:
Catelyn’s mouth grew tight. “Littlefinger,” she murmured. His face swam up before her; a boy’s face, though he was a boy no longer. His father had died several years before, so he was Lord Baelish now, yet still they called him Littlefinger. Her brother Edmure had given him that name, long ago at Riverrun. His family’s modest holdings were on the smallest of the Fingers, and Petyr had been slight and short for his age.
His lordship wasn't much to behold — the land is "mostly rocks and sheep" as one Redditor put it — so he set his sights for higher vistas, eventually becoming Master of Coin on the Small Council. But after his grip on King's Landing became tenuous (ahem, King Joffrey), he manipulated his way into a marriage with Catelyn's sister Lysa Tully, who was the recent widow of Jon Arryn, Lord of the Vale. That made Baelish Lord Protector of the Vale and, after earning her region's trust, Littlefinger swiftly shoved Lysa out her own Moon Door and used his influence to sway her young son Robin Arryn, Lord Paramount of the Vale.
Most usefully, Littlefinger convinced Robin Arryn in Season 6 to send the formidable Knights of the Vale to Sansa's rescue in the Battle of the Bastards. Jon Snow was moments away from losing to Ramsay Bolton when the Knights of the Vale came riding in at the eleventh hour to crush the Bolton armies. Littlefinger isn't exactly the most honorable man in the Seven Kingdoms, but up until now, he's been pretty on point in making sure Sansa remains in power.