Can you change the location of azure-pipelines.yaml in Azure Devops?

While creating a pipeline just click on default file name (azure-pipelines.yaml) and this will make it a text editable and rename location/folder path according to your need.

The UI has changed a bit so it's now under the Settings sub menu of the pipeline:

This solution also works for the cases when you simply want to rename the YAML file to whatever you believe is more appropriate rather than default azure-pipelines.yml. For instance, you might have several builds in the same repo: build_asp_net.yml, build_docker_image.yml, etc.

yes you can do that, when creating the build use old UI wizard, if you already have a build in place, you can open its settings>variables (or triggers) and then navigate to the YAML section and under YAML file path you can change it

click the ... on the build edit page next to the Run button:

The YAML file from a subfolder may be chosen on the third step of pipeline creation wizard.