If anyone born in Sweden has a patronymic name that is usually what they should have as Last Name At Birth. In the period of abt 1850-1900, it started to change, mainly in the cities.
It seems that some of the children of Anders Johan actually uses Gren, Edvin Ferdinand for example who is born as late as 1893. It's spelled Gren and not Green in Swedish, and since Anders Johan never left Sweden that is how he would have spelled it. You can check the household record for 1925-1941 at Swedish National archives,
https://sok.riksarkivet.se/bildvisning/F0006772_00114 You need to register and sign in for this time period but it is free to register.
Some persons were given a different name if they became soldiers and some would take another name if they finished learning a craft like a shoemaker or a carpenter.
Check out the category for Swedish names, I'm sure there are some free-space pages there with information you might find useful;
https://www.wikitree.com/wiki/Category:Swedish_Names