Should his girlfriend pay rent?

One option.

He pays the mortgage. They split the bills. She pays him something towards the interest on the mortgage to recognise that she’s getting a benefit from it. She then puts what would have been the rent payment into her own savings account.

They’re both building assets in their own names, him through paying off the mortgage her through building cash savings. They’re both contributing to the mortgage interest so there’s no free loading.
They split the rest of the bills. There’s no hard feelings about him gaining equity at her cost, or her gaining from him as everyone is in similar position.

Paying rent does not mean she has a claim on the house if it’s in his name…I speak as someone who knows!
It would require a lengthy court battle on her behalf and she would likely lose.

You never know if a relationship is going to last though. It could last a year, or five years, or twenty years, or forever.
I don't think the relationship will last if they want to stay together but she is never on the mortgage and just pays rent. It will just be a trigger for arguments. But you can ring fence deposits.
I have a son old enough to buy a house and I would not advise him to charge his girlfriend rent.

So he pays the mortgage and she pays him rent you mean?
No i don't think that's fair actually. She's his partner not a lodger. She's right that if she is to pay then she should be on the mortgage too. Otherwise she is helping him pay for a house she doesn't own.. will she have her own bedroom like a lodger?
I don't think that set up works tbh.
Hed have to pay the same amount of mortgage were she there or not. And he will own the house at the end of it not her.
He's not her landlord.
Obviously she should pay for half of all expenses like food and bills.
But I do think it's wrong to take rent off a romantic partner if it's going on a mortgage.

And what if he were your son? Would you want his girlfriend to profit from having a boyfriend - because not paying rent, getting a house you haven't paid for or getting cheaper living because your boyfriend has money is "profiting" from having a boyfriend.

We all want what's best for our child. We'd all love our daughters to be given free houses. That doesn't mean it's fair and it's certainly not normal to expect OP prioritise the girlfriend over her own DS.

Maybe DIL wouldn't forgive OP for prioritising her own DS when giving advice but maybe the DS wouldn't forgive her if OP gave him bad advice to prioritise his girlfriend instead of her own child. I'd be furious if I got burned because my own mother gave me advice that benefitted DH and not me.

I think if she were my daughter I’d wonder why her boyfriend would want to profit from having a girlfriend, charging her to build an asset for himself rather than treating her as a partner. He should absolutely protect his deposit but I think it’s a bit harsh if they are in a serious relationship to not put her on the mortgage. Ultimately she could be your future DIL and she won’t forget if this is the kind of advice you’ve given your son. I’d let him decide for himself how to proceed if I were you.

Id give her a tenancy agreement.

She shouldn’t be living their rent free. But he need to document it’s rent she is paying and she isn’t contributing to his mortgage.

If he’s old enough to buy his own house he’s old enough to decide if he wants his girlfriend to pay rent or not

I'd rent it out, and rent somewhere else with her myself. Saves any of that messiness!

Whether or not she pays rent is between them to determine. Fairness depends on a whole load of factors we don't have access to.

Whether or not she pays rent, there needs to be a clear, written, witnessed agreement that she has no claim to the house. No right to stay there if he asks her to leave, no right to any equity in it. If she pays rent, without this agreement, she could argue she contributed financially to the property and is entitled to some of it. If she doesn't pay rent, without this agreement, she could argue he's been financially supporting her and is entitled to on-going relief/support.

tbh it is better if she does not pay rent. If she does, and they split, she could potentially have a claim in that she’s paid towards it. It would be better if she paid the food bill or gas and electric etc but not directly rent towards the mortgage. She could argue that she’s paid into the house and make a claim.

He needs to involve a solicitor and have a legal agreement in place clearly stating that she does not have an ownership stake in the house and how much rent she will pay and share of bills and how any increases in rent will be calculated.

It's increasingly common for people to protect their property legally because it's such a huge investment. Statistically a relationship is more likely to break up than stay together so protect your assets.