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The axis aren't easy to edit, and the format you are constrained by are a bit restrictive, but essentially you need to rename the axes by taking your query:
AzureStorage_CL
| where ResourceGroup == "rg-sdl-adw"
| where PercentClientOtherError_d > 0
| summarize AV = any(PercentClientOtherError_d) by bin(TimeGenerated, 30m)
| render timechart
Now add in an extra line to rename the axis | project-rename NewAxisTitle = AV where the NewAxisTitle is your desired name, and the AV is your old name:
AzureStorage_CL
| where ResourceGroup == "rg-sdl-adw"
| where PercentClientOtherError_d > 0
| summarize AV = any(PercentClientOtherError_d) by bin(TimeGenerated, 30m)
| project-rename NewAxisTitle = AV
| render timechart
Be aware that any time you refer to the axis after the point you rename it you need to refer to it as it's new name.
Hope that all makes sense.