Teacher Recommendation Letter has College Name in it

I invited a teacher to write me a letter of recommendation on the common app. At the time I had only selected one college. My teacher submitted the letter and mentioned that particular college. Does that same letter get sent to every college that I invite them to? If so, can that letter be deleted by the teacher and reworded to be used for all the colleges?

Yes.

The Common App’s answer:
https://appsupport.commonapp.org/applicantsupport/s/article/What-if-I-made-a-mistake-on-a-form-How-do-I-have-that-corrected

Thank you!