When Sansa first meats Petyr in Game of Thrones, Arya asks him why he is called "Littlefinger". He answers that it was because he was very small as a boy and because he lived at the Fingers, now as a boy he lived in the Fingers as he just pointed out so the only people who would have seen him as a boy were also from the Fingers so I doubt they would have teased him for it. Aside from that it doesn't seem like a name that would stick in Westeros, he has been called far wittier names, "whore monger" being one of many. So I was just wondering if that was the actually reason for his nickname or if he was lying to Arya. If he was lying then what is the real reason?
He didn't lie, although you need to remember that he didn't spend most of his childhood in the Fingers, but in Riverrun, where he was fostered. He received his nickname there.
From GoT Wiki:
Petyr Baelish is the head of House Baelish and the lord of an extremely minor holding, so small it has neither name nor maester, located in a small area within the Fingers, a coastal region in the northeastern shores of the Vale of Arryn. In reference to his family's humble domain in the smallest of the Fingers, as well as his small size, Edmure Tully nicknamed him "Littlefinger" when they were children and Petyr was fostered at Riverrun. The nickname would stick with him throughout his life. Eventually even Baelish sarcastically embraced the nickname, due to the fact that it demonstrated how far he had risen, from a poor minor noble from the "little Finger" peninsula to one of the most powerful officials in the Seven Kingdoms.