I wasn't able to find this information in the Hyperspec or Common Lisp: The Language (second edition). Implementation-dependent constants like LAMBDA-PARAMETERS-LIMIT and CALL-ARGUMENT-LIMIT, but not something like SYMBOL-NAME-LENGTH-LIMIT or perhaps PRINTABLE-SYMBOL-NAME-MAX-LENGTH.
The standard symbols with the longest names are UPDATE-INSTANCE-FOR-DIFFERENT-CLASS and UPDATE-INSTANCE-FOR-REDEFINED-CLASS, both 35 characters long, so I suppose that 35 could be taken as a maximum. I don't expect to ever name a symbol something longer than that, but it could matter some day.