Does it matter? Am I over thinking the situation again?

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I study in one school full time and in another part time. Both are graduate schools. My bank manager likes to update the accounts frequently. So he asked for my information, and also asked about my schools. I told him I study in school B part time and in school A full time. School B has a better known name. He went, ok, I put school B as your school.

I was thinking maybe the full time school is the one that matters. I asked my friends and they went all like laughing at me, and told me I was trying to brag about my part time education in a better school and that I should go back to the bank and have the guy change it.

I'm wondering, does it even matter?

Does it matter? Am I over thinking the situation again?