Question about bastards

I think a bastard could marry someone with a name and they would take that name from them. Thats one method. Another is just making up a new name, moving elsewhere in the kingdom and starting over without the stigma.

Thank you! That was informstive. I don’t know why I was thinking about it.
So if Ramsay hadn’t been legitimized and he married sansa would he then be Ramsay Stark?

Yes. Although, technically Ramsay should have been Ramsay Stark anyways since Sansa is of higher social standings and birth even if he had been trueborn, inaddition to being the trueborn heir of a greathouse / rightful queen of the north, andhe was marring into her blood line, not the other way around. 

It would be like a member of House Dayne marrying Arianne Martell. Arianne wouldnt become a Dayne, her husband would become a Martell, because she is of higher standing, and the heir to Dorne. Where the Dayne's are a lesser noble house. 

Dorne really is the only example in westeros of how marrying a female ruler of a great house is supposed to work, since usually eldest daughters are married off to eldest or second sons of other houses, or if their husbands come with little, they, and their new husbands are gifted lands and an holdfast and basically form a cadet branch - Which is what would have likely happened to Arya, she would have ended up married to a second or third son of a lesser house, or even a knight of some sort and her father would have granted lands and a hold fast to her and her new husband. 

“Ramsay Stark” is a perversion if I’ve ever seen one 😒 the names belong nowhere near each other

Ah... I think we can toss this one up as "The Less people that know the better" as a short answer. 

Long answer is, Ned likely did it to protect his wife and children. If Jon's true parentage was ever discovered, then ideally only he'd take the fall for it since no one else, not even Jon himself knew. You also have to take into consideration that when Ned brought home Jon, the last time Ned had seen Catelyn was when they had married, - he had married a woman he didnt know, whom he didnt love, and one that was supposed to be his brother's wife. Ned chose his promise to his dead younger sister, over honesty with his new wife whom was a stranger to him. 

In addition to that, as coldly logical as this is and would have been for a painfully honorable man like Ned. Catelyn's treatment of Jon, being as it was, helped sell the idea that Jon was his bastard. Even after Ned had come to love, trust and respect Catelyn, telling her would have changed the way she viewed and treated Jon. and after years of her scorn, such a change would have been noteworthy and would have sent tongues wagging. 

Mind you, this is all speculation and guess work based upon what we know of Ned's character and personality. - I think Ned never ever intended to tell Jon, or anyone the truth. He intended to take the secret to his grave. Because the truth would have sparked a war of succession, or at the very least a civil war, with his family caught in the middle. - Robert, had he known, would have marched on the North to kill the "Dragon Spawn" - a young man he would have seen as the child of rape, and the cause of "his" Lyanna's death, directing all his rage at Rheager and the Targaryens on Jon.

And those who were unhappy with Robert's rule, would have seen Jon as a chance to rebell. 

Again, all speculation and guess work, but educated guess work. 

I'm not sure if i remember it correctly but i believe bastards are forbidden from marriage and ownings things.

Only if the father (or mother?) Legitimates and allows them to use their name could they marry and have children.

I've never understood why they didn't do this already (moving to somewhere else). I guess for this type of time period, only the higher up classes would be able to afford to move from where they are currently at. For bastards of higher lords, I'm assuming that their looks would indicate that they are bastards of a lord even if they took a new name.