Sure, if you don't want any stake in the property and are just topping up the deposit/her trust fund money as a gift, both the ownership of the property and the mortgage could be in her sole name (so long as the mortgage is assessed as affordable based on the rental yield) - but it would then be her legal responsibility to pay it, not yours. I totally understand your desire to protect this money and make sure it's invested sensibly and not frittered away, but a BTL is not the only way to make sure the money is 'safe' and earns an income/grows while she decides what she wants to do and where she wants to live in the future. For instance £20k is a nice amount to invest in a stocks and shares ISA, I have roughly that amount in a managed fund (entirely passive, I don't have to make any decisions other than indicating my overall risk appetite and reviewing once a year) and it earns/grows a nice little bit each month, maybe £100 pcm entirely tax free, although it fluctuates up and down a bit - and that's with it set at medium risk, you could get a better yield still if you are prepared to risk more?
Yes you might 'earn' more with a property investment in terms of headline income but once the mortgage is paid, tax paid, agents fees, insurances and other costs paid, maintenance and repairs accounted for etc it might not come out much more profitable and that's with considerably more effort put in, plus the fact that the major benefit with the ISA is if I want/need access to the cash I can have it in my bank account within 48 hours whereas if your DD ever decided she needed to sell out of the BTL it would likely take up to 6 months to market and sell the property including evicting the tenants, potentially even longer which could be a major PITA.
Also if you don't want your DD to have the responsibility of a mortgage, you'll have to ensure you have enough money yourself available to cover it in full each month even if tenants stop paying rent or you have extended void periods - and then what would happen if (god forbid) anything happened to you or you lost your income? Plus you paying the mortgage on a house you don't own has the potential to get messy legally speaking although parents do do this for their children all the time of course...
I don't want to sound too negative, obviously BTL can still be worth it in certain circumstances and particularly if you are in an area that is likely to see major/above-average house price growth, and/or if you think it's highly likely your DD will actually want to live in the property herself at some stage. But BTL tends to work best as a long-term, 10 year + investment since the upfront costs are high, and so much could change in your DD's life in that time I'm not absolutely sure it's what I'd choose in your shoes...