Nurse characters named Lieutenant Murphy appeared in two episodes in Season 2 of the M*A*S*H TV series but they were probably meant to refer to two different persons. The first appearance, in "For Want of a Boot" was played by Susanne Zenor while the second, just three episodes later in "As You Were" was the fifth of many nurse characters to be played by Bobbie Mitchell.
Susanne Zenor's Nurse Murphy[]
In "For Want of a Boot", Hawkeye needs to arrange a chain of favors to secure a new pair of boots. One of the favors is to throw a surprise birthday party for Frank Burns. So Hawkeye and Trapper approach Radar for a birthday cake. In exchange for a cake, Radar wants a date with the newly arrived First Lieutenant Murphy, whom he describes as "the big blonde lady" and whom Trapper calls "the wonder nurse".
Trapper and Hawkeye try to convince Radar to try someone easier to approach. Hawkeye says Murphy is "at least two people taller" than Radar and he should "start in the "Boy's Department" and work his way up. They suggest Nurse Anderson ("built like a brick hospital") or Nurse Jacobs ("She's offered her body to science time and time again."). Possibly they are referring to Lieutenant Sheila Anderson and Lieutenant Jacobs who both appeared in earlier Season 2 episodes but the physical description of Anderson does not seem to match. No dice. Radar insists on Murphy.
After a session in O.R., Hawkeye and Trapper meet Murphy in the scrub room but she pushes them off saying she is tired and whatever favor they want, the answer is no. They plead with her, saying they just want to borrow her body for an evening, her heart does not have to be in it. Trapper says they want her to date a "shy Gary Cooper-ish type" and Hawkeye adds "more ish than Cooper".
Murphy surprises them by suddenly saying, "Ok!" but only on the condition that the date comes with a salon style hair dryer. She doesn't need to know who the date is because "for a hair dryer, I'd even go out with Radar O'Reilly".
Hawkeye and Trapper are next forced to approach Klinger as he is the only person around with a hair dryer and, of course, his price is his Section 8 discharge, which needs signatures by 4 officers. Hawkeye and Trapper promise to get it.

Murphy - two people taller than Radar - about to throw him out.
So all is arranged, Radar delivers the cake and the party for Burns is set up. Murphy gets her hairdryer and awaits her date. But things begin to unravel when Frank, although drunk, refuses to sign the Section 8. Klinger gets angry and goes to Murphy's tent to remove the hair dryer. Just as Klinger is leaving, Radar arrives with a bunch of flowers. "And what are you doing here?" she demands. Radar explains that he is the date. "Not unless you plug yourself in and blow on my hair!" she says, and promptly throws him out. Radar goes back to the party to roll the cake away and everything goes downhill from there.
Bobbie Mitchell's Nurse Murphy[]
In "As You Were" there is also a Nurse Murphy. Although this is only three episodes from the previous appearance, this is probably a different character. Besides being a brunette compared to Zenor's blonde, this Murphy is also not aloof and unapproachable. Instead, she engages in banter with Hawkeye. When they meet in the scrub room after a long O.R. session, Hawkeye tells her his hands are raw from all the scrubbing. Murphy tells him,"Why don't you see a doctor?" Hawkeye responds, "How'd you like a swift kiss in the mouth?"

Bobbie Mitchell plays the other, more approachable Murphy in "As Your Were".