If you don't make the new guy an asshole, its actually a great setup for a comedy.
The new guy is probably a HUGE fan of the original heroine, enough to take up her mantel when she is presumed dead. He is likely to be more happy than anyone to find out she is back.
He also happens to be a more powerful hero than her, and has become super famous in her absence. Enough so that even if he tries to give up the borrowed name, the media keeps calling him that anyway.
Obviously you team them up, perhaps reluctantly in the case of the heroine but the hero REALLY wants to adventure with his idol. Together they fight crime, with the heroine having to come to terms with the fact that she isn't the top dog anymore and remembering that she didn't get into saving people for the glory, while also getting some moments where you genuinely get to see how she earned her reputation in the first place.
Bonus round: the fanboy hero that took her name doesn't realize he is stronger than she is, blinded by his fanboyism, and keeps expecting her to be better at him than a lot of stuff. Which sometimes mean expecting her to punch well above her weight against villains because HE can do that and he can't get it through his head thats he's the stronger one of the two