I want to know what security vulnerabilities could have a website that in the name field there is no character limitation. so there could be 100 characters or 10k. My first idea is that it can could lead to DoS to the platform and other users but is that true? are other issues to be concern?
It is not really relevant if there is a size limit in the HTML form fields. Such size limits are only a client side restriction which is also only enforced by some clients (browsers). As with other checks done only at the client-side it is easy to write a client which ignores such restrictions.
All what is relevant in this case is how the submitted data are handled on the server side and this can not be determined just from looking at the HTML at the client side.
It can increase chances of buffer overflow attacks against your code, against the web server, or against the underlying OS.
Also if you happen to end up with a XSS or SQL injection vulnerability on that field, your lack of a length limit gives the attacker full reign to inject any content they want including large scripts like keyloggers or even full encoded binaries for example.
It's safer to enforce max length on all fields server side.