Yes. You can deduct any "ordinary and necessary" expenses of your business that you actually pay, regardless of who's name the bill is in.
The costs of a phone may be a business expense, but only the additional costs in using the phone for business are deductible. If you pay a flat rate on a phone used for business and personal calls, the tax court has held that the flat rate is for your personal phone and you incurred no additional charges for business use. You have no deduction. (TC Memo 2007-151).
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