They actually had ten children (Rembrandt apparently was the 9th child of the ten children that were born from this marriage) so added it to the profile now as well, and added the Geni Family tree to the sources section for now, because we can use sources like this for leads but if they don't cite primary or very reliable secondary records/sources we of course don't know how accurate things are, but we can check if things can be verified in the archives of course. ;)
And yes if they followed or were naming the children according the Dutch naming tradition it would be very logic the first son was named after the paternal grandfather who was named Gerrit. We were (and still are) still looking for records for Rembrandts siblings so we can create profiles for them, so that's why just a few are listed yet.
Now what isn't very logic is that Gerrit would have had a son named Gerrit that would have used the probably patronymic (?) Rutten.
If Gerrit had a son named Gerrit, that son's patronymic (a patronymic is the first name of father + ending s, sz, sen, szen, en or for girls dr or s, en etc. the ending often depends on time and place) would be Gerrits or Gerritsz not Rutten (Rutten, Ruttens or Rutsz)...
So the, most likely also a patronymic, Rutten, is probably telling us that Gerrit Rutten was a son of a father named Rut or something like that...if so and if they still used the Dutch naming tradition, he probably would have named his first son Rut again who would have used the patronymic Gerritsz again ..and so on.
Using the Patronymics and naming the children after the grandparents was done because they believed this way their ancestors would (sort of) live on forever, this also is why if for example the first child died young the next child would again be named after the grandparent the deceased child was named after, and if that child again didn't survive childhood, they again would name a child after the same grandparent. So these later children were not named after the siblings that died young, but after the grandparent and to make sure he (or she) still would live on forever. (In some families including my own, because of this naming tradition, names and ancestors can be traced back for hundreds of years)
And the names and patronymics often are repeated trough out all branches (so all siblings normally would name the first sons after the paternal and maternal grandfathers and the first daughters after the maternal grandmothers) which as you probably can imagine can make things very hard to research or confusing if they only used patronymics...
We can try if we can find more records for all children, perhaps there was a son named Rut (Rutger ?) as well ?