I downloaded a mod which I want to possibly add and the name of the esp and bas is (MyMod)

Is it all right to change the name of them, to something which is a bit more or a representation of what the mod does/adds without any possible side effects?

It is ok, but possible issues are as follows:

Facetint textures and meshes are stored in folders named after the ESP. (CTRL F4 grey face bug stuff)

Voice files are stored in folders named after the ESP.

SEQ file is named after the ESP.

Could be more but those are the ones I have to change with each update. I have one mod with two versions named differently.

The biggest issue of course is if you already have the game saved with the current esp. Changing the name will make the game treat it as though you uninstalled the original. The renamed copy will be assumed to be a brand new mod.

I've been doing it for 12 years. If you follow the guidelines mentioned by B1gBadDaddy and Arthmoor you shouldn't have any problems.

All right, that shouldn't be a problem then. Game hasn't seen the mod yet so won't have to worry about that, and as for also renaming the other folders and files, that's east as well...as long as there ain't to many. Thanks for the info guys