"if I would be flagged for showing contributions to one HSA, when the funds actually went into a different account."
No, this is not a problem.
If you have two HSAs (as you appear to have), for purposes of your tax return, you treat them as one "virtual" HSA. That is, for the code W amount in box 12 of your W-2, and the direct contribution that appears on line 13 of Schedule 1 (1040), you don't actually identify the account numbers of the HSA accounts - you are just working with the "virtual" HSA.
If you find that you have no reason to have two HSA accounts, you can roll one over into the other tax-free. For convenience, you will probably have to keep the one that your employer helped you set up, because they probably won't want to contribute to your other one.
Remember that in any case, both HSAs are YOUR accounts - your employer has no control over them. When you leave your employer, you get to keep your HSA, in just the same way that you can keep an IRA (IRAs and HSAs share some similarities).
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