Considering both would be responding to certain commands that cannot be turned off, it's really a moot point.
Why not just run one bot on DeepBot and the other using something like mIRC to act as a chat logger? You would need to make a few tweaks via scripts to enable certain features (like knowing who is a regular viewer, sub, turbo, mod, staff or streamer) but it can work. Of course you can (and should) use only one bot name connecting from multiple sources (one connecting via DeepBot, another through mIRC, etc), but that's only if it's feasible to do so. If there's a reason that running more than one under the same name isn't an option, then obviously you use separate names.