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With sufficient permissions, you can propose synonyms at http://stackoverflow.com/tags/bug-tracking/synonyms. I see no reason for this process to be overridden for a tag that's not obviously the exact same thing.
They use the icon because YouTrack sponsors those tags, not because StackOverflow just decided arbitrarily to associate the icon. This is one way that StackOverflow makes money.
There is a lot of discussion about these topics in the sponsored-tags tag, including Should tags that represent concepts be sponsorable?
I will add that it seems at least some tags can (apparently) gain sponsored links without logos on the tags — see cms
Issues are not bugs, but bugs can be issues.