Disclaimer: I am not a financial / legal / tax advisor. This is not such advice.
TL;DR: A lot may depend on where the minor's money came from. If they have earned it themselves (or it was gifted by other than a parent), there should be no problem. If it was originally gifted from a parent, then any savings interest income over £100 (and possibly other types of income) could place the tax liability on the parent.
Many sources attest that children/minors are treated for tax-purposes the same as adults: they have their own allowances and are liable for tax if they exceed them. For instance, the article Minimising Tax When Investing for Children by Hargreaves Lansdown includes:
The child's tax position
Most children can ‘earn’ up to £18,500 per year without incurring tax (personal allowance of £12,500, starting rate for savings of up to £5,000 and personal savings allowance of £1,000).
They will have a Capital Gains Tax (£12,000) allowance as well. This means that while their investments may be taxable, there is often nothing or very little to pay. The numbers quoted apply to the 2019/2020 tax year.
However, several also warn that if income is derived from money gifted by a parent then only the first £100 can be "swallowed" by the child. Above this amount, it all counts towards the parent(s)'s tax affairs. From the UK Government's Interest on savings for children page:
There’s usually no tax to pay on children’s accounts.
Tell HMRC if, in the tax year, the child gets more than £100 in interest from money given by a parent. The parent will have to pay tax on all the interest if it’s above their own Personal Savings Allowance.
You must also tell HMRC if a child has an income over their Personal Allowance, e.g. from a trust. The child will have to pay the tax on this.
The £100 limit doesn’t apply to money:
- given by grandparents, relatives or friends
Much less is said on Capital Gains in relation to money/assets originally gifted from a parent; the closest I could find is from the document Investing for Children Part 2 produced by the Chartered Insurance Institute (CII):
The tax rules briefly described in part one of this two-part article1 mean that there are opportunities to take advantage of a child’s personal allowances and capital gains tax (CGT) annual exemption when investing for children. However, when parents make gifts for the benefit of their own minor unmarried children, not in a civil partnership, greater care is needed in finding a tax-effective solution given the anti-avoidance rules that exist (where income generated from parental gifts to a minor unmarried child not in a civil partnership, on all gifts from the same parent, exceeds £100 gross in a tax year it will be assessed to income tax on the donor parent– the so-called “£100 rule”).
However, if the money is not a parental gift, this should be of no concern.
In either case, your description and the DeGiro pages suggest that what you would be setting up is a Designated Account. The aforementioned CII document lists this as one of three ways investments can be held by, or made for the benefit of a child (the others being "Earmarking", which seems to have little tax benefit; and creating a legal trust for the child: several types, each with the own benefits and drawbacks).
As far as a Designated Account is concerned, the CII document has, variously:
Stocks and shares and collective investments (i.e. unit trusts, OEICs and investment trusts) are sometimes held by way of a designated account. A designated account enables investments to be bought by an adult (such as a parent, guardian or grandparent) and the investments are designated in the name of the child.
Under English law2, and if there is nothing to the contrary stated, such an arrangement will normally constitute a bare trust under which the investor i.e. the purchaser of the shares/units, will be the trustee and the beneficiary (beneficial owner) will be the designated child.
In the HMRC Capital Gains Tax Manual at CG11730 it is stated that ‘it is the beneficial ownership (not legal ownership) which the tax principally follows. In its Trusts, Settlements and Estates Manual at TSEM 9150 HMRC clearly recognises that legal and beneficial ownership can be separate.
So a Designated Account is similar to an Absolute (Bare) Trust but (providing you are only dealing in stocks and shares) offers some advantages:
(i) It is simple to set up and there is no need to inform HMRC of its existence.
(ii) There are no legal fees.
(iii) No tax returns are required (subject to the £100 rule) until such time as income/capital gains result in a tax charge on a beneficiary.
In summary: If the money is the minor's (or, at least, not a direct parental gift) there appears to be no danger of the tax-liability reverting to you, just because you name is on the "designated account". If parental gifts are involved, and the income from them exceeds £100 (per year) then it is very likely that the tax onus on that portion will fall to the parent.
1 I have not been able to find Part One of the article on the CII website.
2 Any talk of the difference between legal and beneficial ownership only applies to England. Scottish law does not distinguish between the two terms.