If Arianne inherited Dorne in the end and marries someone, her family name will be lost or if Sansa inherited Winterfell the Stark name will change for ever?

racefortheironthrone:

No, not necessarily. As seen with Cersei Lannister, a woman doesn’t necessarily take her husband’s name. 

Also, based on some questions I got, a clarification/extension:

• Dornish custom is that Arianne’s kids take her name, so her family name is not in danger.
• Sansa is a bit more iffy, but there is precedent for husbands and children changing their names to maintain continuity: Joffrey Lydden became Joffrey Lannister when the male line ended early in the Andal period; the Tallharts offered to have Beren Tallhart (whose mother is a Hornwood) change his name to Hornwood if he was named heir, sot hat the line could continue.