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CLT results:
"Richard LeParmentier" is credited in the following 34 titles (104 profiles)
"Richard Parmentier" is credited in the following 23 titles (157 profiles)
"Richard Le Parmentier" is credited in the following 19 titles (75 profiles)
"Rick Le Parmentier" is credited in the following 3 titles (6 profiles)

According to the CLT results, "Richard LeParmentier" is the common name, but looking at the titles listed, several are actually invalid. Between the three names, there are many overlaps. I've put an asterisk next to titles that overlap in the CLT results.

Richard LeParmentier - 0 confirmed

Unconfirmed
Shine On Harvey Moon: Season 1, Episode 1
Stardust (1974)*
We'll Meet Again

Invalid:
Lillie, Episode 9
Octopussy
The People That Time Forgot
Reilly: Ace of Spies, Ep 10
Rollerball (1975)
Silver Dream Racer
Space: 1999: Season 2, Ep 21
Star Wars: Episode IV: A New Hope
Who Framed Roger Rabbit

Richard Parmentier - 8 confirmed
Confirmed:
Hammer House of Mystery and Suspense: Paint Me a Murder (confirmed by me)
Lillie, Episode 9 (confirmed by me)
Octopussy (confirmed by me)
The People That Time Forgot (confirmed by me)
Reilly: Ace of Spies, Ep 10 (confirmed by me)
Return of the Saint, Ep 11 (confirmed by me)
Silver Dream Racer (confirmed by me)
Superman II  (confirmed by me)

Unconfirmed:
Hazell: Series 2, Ep 10
Master of the Game
The Professionals: Series 3, Ep 4

Richard Le Parmentier - 3 confirmed
Confirmed:
Space: 1999: Season 2, Ep 21 (confirmed by me)
Star Wars: Episode IV: A New Hope (confirmed by me)
Who Framed Roger Rabbit (confirmed by me)

Unconfirmed:
Capital City: Series 1
Capital City: Series 2

Invalid:
Rollerball (1975)

Rick Le Parmentier - 1 confirmed
Confirmed
Rollerball (1975) (confirmed by me)

Unconfirmed:
Stardust (1974)*

Thanks to Amazon instant streaming, Netflix, and Youtube, I've been able to get quite a few more confirmed. Unless I missed a few titles, it doesn't look like any other name will be able to catch up. Richard Parmentier appears to be the current winner.

Thanks!

Richard LeParmentier - 0 confirmed
Shine On Harvey Moon: Season 1, Episode 1
We'll Meet Again

Richard Parmentier - 10 confirmed
Hammer House of Mystery and Suspense: Paint Me a Murder (confirmed by me)
Hazell: Series 2, Ep 10 (confirmed by Rutan)
Lillie, Episode 9 (confirmed by me)
Octopussy (confirmed by me)
The People That Time Forgot (confirmed by me)
The Professionals: Series 3, Ep 4 (confirmed by T!M)
Reilly: Ace of Spies, Ep 10 (confirmed by me)
Return of the Saint, Ep 11 (confirmed by me)
Silver Dream Racer (confirmed by me)
Superman II (confirmed by me)
Master of the Game

Richard Le Parmentier - 5 confirmed
Capital City: The Complete First Series, multiple episodes (confirmed by T!M)
Capital City: The Complete Second Series, multiple episodes (confirmed by T!M)
Space: 1999: Season 2, Ep 21 (confirmed by me)
Star Wars: Episode IV: A New Hope (confirmed by me)
Who Framed Roger Rabbit (confirmed by me)

Rick Le Parmentier - 2 confirmed
Rollerball (1975) (confirmed by me)
Stardust (1974) (confirmed by SoylentDave)

Hazell: Series 2, Ep 10 Richard Parmentier as Mort Berman