The 33-year-old captioned the video which she shared with her 76 million Instagram followers, "Happy One Month True".
"Happy One Month True", Kardashian captioned the clip.
True was born in OH on April 12.
True's grandmother Kris Jenner revealed after she was born: "Fun fact ... my Grandfather's name on my Dad's side was True Otis Houghton ... my Dad's name was Robert True Houghton ... so I am so excited Khloe named her daughter True!"
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West Australian Police Commissioner Chris Dawson said the children's father, Aaron Cockman, had been notified of the tragedy. All the victims appeared to be residents of the property , police said, but did not explain how they were connected.
Her baby girl True turns a month old today.
"Things are more complicated now that there is a child involved, but it was causing more stress on Khloe by being in limbo with Tristan".
The lone Kardashian brother is still furious with Thompson, according to a report by TMZ. Despite the mixed emotions fans are well aware that having a family has always been top on Khloe's list of priorities.
However, those close to Rob also say that he is ecstatic to have a new niece in the family, and he can't wait to meet baby True. Reportedly, Rob plans to be the uncle that will spoil baby True.
Kardashian and Thompson have yet to address their relationship status, although Kardashian attended Thompson's basketball game Saturday.