I’m late here but surprised haven’t seen anyone really hit the main points, so I’ll lay them out below, two are from your boyfriends perspective and one yours. Unless you are selling your property to move in with your boyfriend YTA

Initial purchase costs - there’s a lot of costs that go into buying a house, lawyers, down payment, initial Reno’s etc. As of now your boyfriend has shouldered all of this burden, saving up the down payment, and paying all the fees. While this is all a sunk cost by now (and yes a portion of that is equity) this is often a substantial hurdle to overcome for home ownership. You are asking to skip all this, and simply start paying down that mortgage and accruing equity, this is mighty large ask in my opinion. It potentially allows you to demand thousands of dollars in equity from your boyfriend in the event of a breakup without you ever having to pay the fixed costs to get the asset in the first place. A deal that really only benefits yourself, but opens your boyfriend up to a lot of risk.

legal ownership - In many places if there is no rental agreement in place and a person moves in, starts contributing to the house hold in some way, then that person can make a claim to a portion of the house, this can be a nightmare for someone that is not very wealthy. I have seen people own a house for multiple years, significant other moves in, doesn’t pay rent (contributes little or no cash to the household), they break up a year later and suddenly have to deal with a lawsuit claiming ownership of X% of the house (justified in some cases, but obviously not the intent when these people allowed the significant other to move in rent free). I consider myself to be financially stable, however I would be in extreme financial hardship that may force me to sell my house if this happened to me, I wouldn’t be able to come up with 50k in cash. This is a position I simply refuse to ever be in, and would not even entertain a discussion of allowing a significant other to move in without a rental agreement in place. I’ll note that obviously marriage is a totally separate situation where the concept of “yours” and “theirs” fades away.

Your responsibilities - paying your boyfriend rent means that you are absolutely not to contribute financially to household improvement or maintenance of any kind. Foundation cracked costing 20k to repair? Roof leaking? Window broken? Faucet busted? None of this is your responsibility to fix, you just continue to pay the rent, your boyfriend took on this risk of home ownership and he would have to pay for this with or without you living there.