Goddess Parvati was never the daughter of Bhrigu. She is Adi Parashakti incarnated as Lord Shiva's wife and from her emerged the 10 Mahavidyas of which the last one is Kamala or Lakshmi. And Lakshmi is Bhargavi and that's how Parvati's one name is also that.
The story of how the Dasha Mahavidyas emerged from Adi Parashakti/Sati/Parvati is given in Devi Purana and is detailed already in the answer here.
Quoting from that answer:
Once the greatest of Yogis, Lord Maheswara worshiped MahAdevi and
obtained from her the boon that She will be his wife. Lord Brahma upon
realizing that soon MahAdevi will manifest herself as per the boon,
orders one of his favorite sons, Daksha, to engage in penance so that
the would be consort of Lord Shiva can be his daughter.
Daksha thus did a severe tapasyA to MahAdevi and she appeared before
him. When asked what boon does he want, Daksha said he wants MahAdevi
to be born as his daughter. MahAdevi granted that boon and said when
she will descend to be the wife of Lord Shiva she will take birth from
Daksha's wife Prasuti's womb. But she also reminded him that once
Daksha's merits end or if he somehow disreagrds her, she will leave
him instantly.
The Daksha Yajna episode is well-known so I am not repeating it in full here. When, Lord Shiva saw that Sati was adamant to attend his father's Yajna inspite of his disapproval got a little angry and reprimanded her saying:
Janami vagvahirbhutAm tvAmaham dakshakanyake |
yatharuchi kuru
tvancha mamajyAm ki pratikshase ||
I know that you are not bound by my orders, so do as you please, why
are you waiting for my consent?
Upon hearing Shiva's strong words Devi got angry. And thought to
hersef that Shiva, upon obtaining her as his wife, forgot her real
form (which is of Parama Shakti). So let me abandon him and my proud
father and stay in my own swarupa and in my own lila for sometime.
tyaktanamapi darpishtham pitarncha prajApatim |
SamsthAsyAmi
kiyatkAlam swasthAnam nijalilAyA ||
On thinking thus, Devi assumed the terrible form of MahAkAli. Which
was of a Goddess who is dark complexioned, digamabari (without
clothes), lolajihvA (tongue hanging out and clasped with the teeth),
with disheveled hair and wearing garland comprised of slain heads.
Lord Shiva was terrified on seeing Goddess's such terrible form and
tried to escape from that place immediately.
Upon seeing her terrified consort Shiva, Devi, out of mercy and in
order to block all the ten directions (so that Shiva can not escape
through any one of them), assumed ten different forms with each
blocking one direction.
Evam patim vikshya bhayAbhibhutakam dayAnvitA tat prati vAranecchayA |
sarvAsu dikshu kshanamAtramadhyataha stithA cha bhutvA
dashamurtayastadA |
Whichever directions Lord Shiva tries to escape through, finds one or
the other terrible forms of Devi guarding there. So, unable to find an
way to escape Lord Shiva closed his eyes out of fear and upon opening
them again found the terrible Goddess MahAkAli right in front of him.
Lord Shiva asked " Who are you ShyAmA (the dark complexioned one)?
Where is my beloved Sati?"
Devi laughingly replied " Can't you recognize me? Iam your own Sati.
Im the SrishtistithisamhArakArini SukshmA Parkriti. For being your
wife I have become fair complexioned (Gauri). The ten Devis that you
see around you are also my forms. Hence, O MahAmati Shambhu, do not
fear:
Sati said to her husband who was afflicted with fear " The Goddess who
is in your front is BhimanayanA MahakAli, in the sky (or in the
antariksha direction) is TArA, on the right side is ChinnamastA, on
your left is Bhuvaneswari, behind you is BagalAmukhi, at the
south-east corner (Agni Kona) is DhumAvati, in the south-west corner
(Nairitkona) there is KamalA, in the north-west corner (VAyukona)
there is MAtangi , in the north-east corner (IshAna kona) there is
Shodashi (Tripura Sundari) and in your own self I am existing as
Bhairavi.
Now, if you want I can teach that proud Daksha a lesson by destroying
his Yajna.
A somewhat different account of the appearance of the Mahavidyas (from Goddess Parvati) is also found in the Devi Bhagavtam which is also given in my linked answer.
So, whatever the story is, the fact is all the Mahavidyas, including the 10th or Kamala, emerged from Goddess Parvati only.
And Kamala is identified as Goddess Lakshmi who again is known as Bhargavi, the daughter of Bhrigu (as shown in this answer). So that's how Goddess Parvati's one name is also Bhargavi.
