I love having the price alerts feature and its one I utilise a lot, but with so many alerts I find keeping track of what they are indicating requires a lot of extra work. Where as if I had the ability to rename or even add a simple buy/sell tag to the alert it would increase the utility of the feature 10 fold.
I know it’s not the same, but until your query gets answered, you have the option to add text notes to your charts which you could use as reminders for your alerts 
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That works until you close the chart and everything is lost.
I concur with the OP and would also like to propose a note facility; basically a title and/or note attached to the alert.