Remus is introducing her in standard form--you say, "Harry, this is Joe Smith," then Joe Smith says either "Call me Joe," or "Nice to meet you" (in which case, you assume "Mr. Smith").
Tonks uses a nonstandard form of address, so it's up to her to clarify what it's going to be. Saying, "Harry, this is Nymphadora Tonks," is the proper way to do it, in which case, she would say, under purely professional conditions, "Call me Tonks. Please."
Instead, Remus gets partway through the introduction, and she cuts him off with, "Don't call me Nymphadora!" which (a) divulges her name herself and (b) establishes that it's a game for Remus to actualy use that name on her... otherwise, he'd just be doing a standard introduction and there would be no need to cut him off. To assume otherwise assumes that she's both stupid (revealing info herself that she wanted hidden) and rude (interrupting an everyday social ritual with a strident demand). She doesn't come off as either.
no subject
Remus is introducing her in standard form--you say, "Harry, this is Joe Smith," then Joe Smith says either "Call me Joe," or "Nice to meet you" (in which case, you assume "Mr. Smith").
Tonks uses a nonstandard form of address, so it's up to her to clarify what it's going to be. Saying, "Harry, this is Nymphadora Tonks," is the proper way to do it, in which case, she would say, under purely professional conditions, "Call me Tonks. Please."
Instead, Remus gets partway through the introduction, and she cuts him off with, "Don't call me Nymphadora!" which (a) divulges her name herself and (b) establishes that it's a game for Remus to actualy use that name on her... otherwise, he'd just be doing a standard introduction and there would be no need to cut him off. To assume otherwise assumes that she's both stupid (revealing info herself that she wanted hidden) and rude (interrupting an everyday social ritual with a strident demand). She doesn't come off as either.