GitHub repository ownership as a PhD student in a lab

It's fairly common for labs to have GitHub organizations. There are multiple reasons for this.

1. First of all, it doesn't prevent the authors from getting credit. The commits will be shown as commits of the individual, not as commits of the organization.
2. Labs often have a scientific "brand" in terms of what they research. If the GitHub repository is completely personal, then your work does not fully contribute towards this brand. But contributing towards the joint scientific output of the groups is a major reason why you may get funding from the group's third party funding.
3. Perhaps most importantly, PhD students eventually leave the lab. They can continue maintaining their projects if they want to - there is no necessity to be an administrator of a GitHub organization to continue maintaining existing repositories. But what if the leaving PhD students choose not to maintain the code? If the repository is personal, then other people in the lab then cannot commit bugfixes to the repository. They could fork it, but once the repository link is in a scientific paper, the original repository is the official one. And this is problematic if the group's brand depends on the repository because it's a central part of their overall story.

For me it boils down to the question: Does the individual student take the software with him after the PhD and build his career on it? Or does the lab base a large share of its work on this code and multiple students will contribute and maintain the code.

An example for single person is Tim Davis' UMFPack / Suitesparse. He wrote multiple articles about the algorithms and further improvements. When he moved from Florida to Texas, he took all software with him.

If your concern is about the future of the software, it depends on the people. If the single developer leaves academia, the project is at danger. If the group maintaining the software cannot motivate new PhD students to pick the task up and continue maintaining, the project will break.

If your audience is non-programmers or infrequent programmers:

Most people will not look at Github accounts or care which account is associated with your code. They will look at the manual. They will look at journal articles about your code. It's possible they might look at a copyright notice.

Write a useful manual, and state at the beginning of it who should get credit for writing the software.