We (ex-we, thank goodness) took in two grey foundlings which I promptly named Smokey and Fagash (UK for cigarette ash). Not popular names so after a few hilarious name pairs (refused) I got a bit cute & suggested we called the tom James and the queen Jesse. Success! till the penny dropped the next day! But by then it was too late.
If you found the mog on a tip why not call her Mary - as in "Tip it up Mary, my fine daughter. Tip it up Mary if you can......"