Jessica Chastain's claim about a popular baby name isn't holdin' water -- while she says lots of fans are naming kids after her "Interstellar" character ... Babynames.com says that's not the case.

The online database for baby names tells TMZ ... the name "Murph" -- Chastain's character's name from the hit 2014 movie -- isn't the big hit she thinks it is.

Babynames.com used the Social Security Office data, and it says "Murph" didn't make the top 1,000 names ... for men or women in any year.

And, the site also says only one person added the name to their favorite name list in the 2 years after "Interstellar" came out, and another added it last year -- so, people aren't even seemingly looking at it as a contender.

ICYMI ... Jessica attended the Breakthrough Prize Honors last Saturday -- and, she told People couples have approached her and said they named their child after her character.

Babynames.com says it's definitely not a widespread trend ... even though it might seem that way to JC.

Not to say Jessica's lying -- frankly, it makes sense someone who named their kid after Murph would likely want to tell Jessica about it, and, to her, it would feel like a growing trend.