Will my personal data on my iPhone be safe when transferring to a new carrier?

Yes, you keep the same Apple ID, you only switch carrier.

and would like to switch to a new carrier.

Will you keep the same phone number?

Will my phone contacts, notes, banking, etc. function as before if I switch carrier?

Yes, if you keep the same phone number.

If you are going to change providers, you are entitled to number portability if you have a subscription.

Subscribers can take their telephone number with them (also known as number portability) to another carrier.

Number portability is handy, you don't have to change anything, you use the same number.

If you use a prepaid or postpaid it is not possible.

If you want to keep your phone number and change carrier, you should have indicated to the 'old' carrier.

You must inform the 'old' carrier that you want to take your phone number with you to carrier X (new carrier).

Your the 'old' carrier will take care of the switch. Informs carrier X (new carrier) about this.

You must declare on time, and keep in mind that you will not be able to use your number for a few days. This all depends on where you live.

If the SIM format is different, visit or contact your 'new' carrier and request a replacement SIM card, normally it is free.

Just a little additional clarification. Your carrier has access to who you send/receive calls and SMS messages from. They have access to location information (based on cell tower use) and they have some access to what you're doing with your data (e.g. they may know what websites you visit). But they don't have any direct access to your notes, contacts, your banking information, your iMessages, your email, your files.

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Thank you for your feedback and you're welcome.