All courts have local rules or even standing orders governing filings and pleadings - from case styling formatting, font/size, spacing, max pages, ect… Federal district courts are not places to flaunt rules of the court or court orders.
Beyond that lawyers are governed by state bars and rules of professional conduct — as an example the Florida bar has taken action against an attorney that used to advertise himself as a “pitbull.”
Regarding tattoos courts have rules of decorum, which generally cover appropriate dress/attire in the courtroom. As far as tattoos, I’ve been to thousands of hearings and can give a single anecdote. It was a drug possession case and the defendant was allowed to transfer their case from circuit felony to drug court - basically allowing completion of drug classes while on kind of pretrial probation in exchange for either a nolle pros (dismissal) or withhold of adjudication. The drug court judge gave the defendant a hard time at this initial hearing over having a drug molecule tattooed on their neck - questioning if drug court was a good fit for someone the seemingly was pretty committed to drugs (based on the neck tat). The drug court judge can see a hundred or more defendants a day, they’ve seen it all and aren’t passing judgement, its just that their experience allows them to read people extremely well and they had legitimate concerns because getting in trouble in drug court can result in automatic conviction of the original charge + having to deal with any new charge.
A rule of thumb professionalism and decorum go a long way in court - this attorney could be decent, but as a potential client any lawyer using a gimmicky dragon in a suit in their paperwork should probably raise some red flags for you.