Hey OP seems like you had enough confidence to ask for her name, which is good and also if you’re nervous; thats completely normally because as someone who stutters also I experience the same thing when talking to girls. Based on what you said you guys seem friendly so my impression is she doesn’t see you as someone who is weird so I think you can slowly make a move but be regular about it. Whenever she compliments you about clothes, you can compliment her back on her clothes to keep the mutual interest. Or if you want to flirt with her a little bit whenever she compliments you about what you’re wearing you can always say “oh really? Thanks I can be your personal designer/get your drip up or whatever if you want…” (something along those lines im making shxt up )THEN you ask for the number or something like that to initiate the contact info. I think you’re on the right track and try to be as smooth as possible (keep a calm head) and try your best not to OVERTHINK what you want to say because that may trigger your stutter.