I tend to use whichever variant or spelling of the name which appears most on that particular person's documents (whatever it is I can find). If a child uses a different spelling variant to their parents, then the child on my tree will probably have a different spelling.
On my Dutch Jewish side one name starts with "van Kollem" or "Kollum-Sofer" and in various places appears as van Kollem, van Kolm, Kolm, Kollum, van Kollum, van Collem, van Colm, Collen, van Collen - and occasionally it also got anglicized to Collins. In some instances, different children within the same family used a different variant of the surname. I usually chose whichever one appears most often on whatever documents I can find. Given that they were also Dutch, I occasionally have places where a "ij" spelling has been altered to "y" such as: "Speijer" to "Speyer".
The most difficult part is when they emigrate... figuring out how they spelled their name (or the enumerator spelt their name) can be difficult. I've never found the death register of my 4x great grandfather because of this - he died sometime before 1841, but his Dutch name was Coenraad Samuel Helschau Leben (or Leben Helschau, I'm not completely sure) but he's often referred to as "Charles Collins" in documents for his children. His anglicized name came from his mother, who was one of the before mentioned "Van Kollem" family, one who maintained the spelling.