First of all I'd suggest that it is really a matter of choice I suppose.
As already mentioned, Genna Lannister was never called Genna Frey despite marrying Emmon Frey. Their children however all carried the Frey name.
Another example which has not been mentioned yet is Lelia Lannister who became Queen Consort of Iron Islands by marrying Harmund II Hoare, is always referred to as Lelia Lannister, not Lelia Hoare.
Yet another example is that Rhaenyra Targaryen, Princess of Dragonstone married Ser Laenor Velaryon, heir to Driftmark and great-grandson of King Jaehaerys I Targaryen. She kept her name Targaryen even though her alleged children with Ser Laenor had surname "Velaryon". But then again, we can say she needed Targaryen name to appear as legal claimant to throne of Aegon the conqueror. Still, it appears to be her choice.
Catelyn Stark had a loving relationship with Eddard Stark so it makes sense that she chose to be called Catelyn Stark, not Tully. Cersei and Robert's relation was never good so it makes sense that Cersei refused to take her Lord Husband's name. But there is no canon source for this and this is just speculation.
That being said, never in the history of Westeros has a Queen changed her name to adopt her Husband's family name.
Queens don't change names
I have never seen any Westerosi Queen taking her Lord Husband's name if she comes from another house. Let's see list of all previous kings and their queens who were not of same dynasty:
King Aenys Targaryen and Queen Alyssa Velaryon
King Aenys married Alyssa Velaryon and took her to his Queen. She is never referred to as Alyssa Targaryen after her marriage.
King Maegor the Cruel & his Consorts
King Maegor the Cruel married multiple times both within and without his dynasty. The brides he took from outside House Targaryen were Ceryse Hightower, Alys Harroway, Tyanna of Pentos, Elinor Costayne and Jeyne Westerling. Notice how none of the five Queens took the Targaryen name.
King Viserys I Targaryen and his consorts
King Viserys I married twice. First he married his cousin Queen Aemma Arryn. After her death he married Alicent Hightower. Both Queens kept their own names even though Aemma Arryn was half Targaryen on her mother's side.
King Aegon III Targaryen and Queen Daenaera Velaryon
King Aegon the Dragonbane married twice. His second marriage was outside House Targaryen with Daenaera Velaryon. The Queen kept her name instead of becoming Daenaera Targaryen.
King Viserys II Targaryen and Queen mother Larra Rogare
Viserys II married a Lysene noblewoman from old blood of Valyria, Larra Rogare. The couple had a troublesome relation. While Rogare family helped Targaryens to stabilize rule of Viserys's brother, Aegon III, Larra never felt happy in Westeros. Eventually, the marriage collapsed and Larra went back to Lys leaving her children, Aegon, Aemon and Naerys behind. Viserys never took another wife even after becoming the King. So even though Larra never became the Queen, she remained Rogare, not a Targaryen.
She died during reign of Viserys II and never saw her son Aegon IV become King but I suppose we can consider her Posthumous Queen Mother on this account.
King Daeron II Targaryen and Queen Mariah Martell
King Daeron the Good married a Dornish Princess Mariah Martell. Queen Mariah kept her family name.
King Aerys I Targaryen and Queen Aelinor Penrose
King Aerys made his cousin Aelinor Penrose his Queen. She remained a Penrose.
King Maekar Targaryen and Lady Dyanna Dayne
King Maekar the Anvil's wife Dyanna Dayne died before his ascension to Iron throne thus never became a Queen. Maekar never took another wife or had any affair afterwards that we know of which hints at a successful marriage full of love (And six princelings). But anyhow, notice how despite never being a Queen, Dyanna is still a Dayne, not Targaryen.
King Aegon V Targaryen and Queen Betha Blackwood
King Aegon the Unlikely married with a woman of comparatively low birth, Betha Blackwood. At time of marriage, Aegon was so below in line of succession (fourth son of a fourth son) that no one objected. But eventually Black Betha became a Queen and her husband one of the greatest Targaryen Kings ever. Betha however remained Blackwood, not Targaryen even though Betha and Aegon married for love and remained in love through out their marriage.
This concludes the list of Monarchs other than Robert I Baratheon who married women of other dynasties. As you can see, there is not a single case in which the Queen consort took her Husband's name or is referred to by her Husband's house. So why should Queen Cersei Lannister take her Royal Husband's name?
The precedent continues. As pointed out earlier, Margaery Tyrell is still a Tyrell despite marrying Joffrey I Baratheon and Tommen I Baratheon. Not to mention she had also married Renly Baratheon in the past. She did not become a Baratheon either. Simple as that, it is evident that Queens don't change their names.
If we move past Royal marriages and discuss general nobility, there are conflicting accounts about it, unlike Royal marriages. Olenna Tyrell was called a Tyrell but she was infact born a Redwyne. Similarly Donella Hornwood was called Hornwood despite being born a Manderly. On the opposite we have many and more examples as cited above where ladies retained their birth names after marriage. So all we can say is that it depends on choice of the lady and her circumstances.
Also another aspect to consider is, the POV. When Masha heddle begs Catelyn Stark, that's Tyrion's POV. When Catelyn calls herself a Tully, that's her POV. When Cersei is called a Lannister, that's Eddard's POV who had previously called the Queen "The Lannister Woman".