If I consolidate my credit cards into one payment, will this give me a bad credit record?

No. Whether you have one, five or ten open accounts, the number does not matter. What determines your credit is your payment history with your open accounts.

If you transfer all your open accounts to one, the only benefit will be the convenience of converting several bills into one payment, which will make paying bills easier. Creditors don't pay too much attention to the number of accounts you have open; what they do take into consideration is how much total debt that you have in comparison to your income. The creditors will make decisions based on whether or not you have the means available to pay back the money that they lend to you.

Just remember that when you consolidate your credit cards into one account, that does not automatically delete your payment history with these credit cards. Your credit report will have your payment history with those recently closed accounts, which lenders will take into consideration in determining whether or not you will be granted credit.