Without knowing how serious your relationship is, it's hard to say.

I would advise not doing this if the main reason is to save money, especially with one person being the sole owner. The power dynamic is too unbalanced.

But if you're both pretty sure this is a long-term, perhaps lifelong, relationship, then no one here can give you the correct answer. Set aside some time, sit down with your partner, discuss things from both a practical and emotional perspective, do this again in another week or two, and find an arrangement you both feel good about.