Putting it in your name would be theft and void your UC, so all kinds of trouble.
You need to open an account in sons name. Either a Junior SIPP or a Junior Stocks & Shares ISA; or both.
You cannot avoid him having control of a savings account when he is 18, the “bank” will write to him when he is approaching 18 telling him about it and require him to setup a new password etc.
When it comes to investing, I can recommend the book “Money : Master the game” by Tony Robbins, but his advice would be the same as the advice Warren Buffett the worlds most successful investor gives to 95% of people:
Buy index tracker funds, they are low-cost and diversified. You can choose an american focused one such as an S&P500 Tracker or a UK one such as a FTSE100 tracker amongst others of course. You can put £9k in a Junior SIPP before April 5th and another £9k in a Junior SIPP after April 5th.
If you have real worries about the age 18 access then maybe open a Junior SIPP (private pension) instead and put £2,880 in each year and HMRC will add £720. You can invest in the same things in a SIPP as you can in an ISA but he won’t be able to access it until in his late 50s.
Doing both ISA and SIPP spreads the risk a bit. If it was me I’d put £2,880 into a SIPP this year and another £2,880 next financial year (after April 5th). The remainder into a Junior Stocks&Shares ISA.
No-one knows what the future holds but I would ball-park or target for the investments doubling every 10 years if all continues as it has in the past. Of course this depends how it is invested, but that £20k invested now could become £640k when he is 61.
Is he a one marshmallow now boy or a 2 marshmallows if he waits until teatime boy? (wait until he’s 18 or wait until he’s 61). I appreciate you need to be led my the will stipulations.
I’m using Hargreaves Lansdown for my son and am happy with it.
Check out MSE: https://www.moneysavingexpert.com/savings/investment-beginners/