peter Slang for "penis" is attested from 1902, probably from identity of first syllable.
johnson "penis," 1863, perhaps related to British slang John Thomas, which has the same meaning (1887).
"fellow, lad, man," 1550s, rhyming nickname for Rick, short for Richard, one of the commonest English names, it has long been a synonym for "fellow," and so most of the slang senses are probably very old, but naturally hard to find in the surviving records. The meaning "penis" is attested from 1891 in British army slang.
The Lover's Tongue: A Merry Romp Through the Language of Love and Sex by Mark Steven Morton has an entire chapter on the subject, "The Long and the Short of It: Words for the Penis and Its Attendant Parts," that begins with an impressive five-page collection of names. Here's what he has on the names in question:
A few years after Edward Ward published his poem, the name Roger also came to denote penis. This was, in fact, the first of several male given names to be bestowed on that part of the male anatomy—Thomas followed in 1811, Dick in 1891, Peter in 1902 and Willie in 1905. To some extent, the application of these names to the penis occurred simply because those names were considered typically male, the kind of name that Joe Blow or any Tom, Dick or Harry might have. [...] With Peter, however, there may be an additional reason why it came to denote penis: that name derives from the Greek petros, meaning stone, a material whose hardness might recall the firmness of an erection. The word is still used with that stony sense in the name saltpeter, a chemical compound that was once given to young men and soldiers to reduce their sexual ardour. [...] Last names, too, have been bestowed on the penis, such as Johnson, which dates back to the mid nineteenth century but has recently gained wide currency.