It depends on what the entity of the salon that you pays to files under. If they are incorporated you don't need to if they are a sole proprietor or partnership you do. Here is more info from a reputable online source.
Issuing Requirements
The IRS requires that you issue 1099s to any independent
contractor who provided at least $600 worth of services to your
business. Many businesses are unsure of the requirements for issuing
1099s to limited liability companies. The answer depends on how the LLC
is treated by the IRS. For federal tax purposes, a limited liability
company may elect to be taxed as a sole proprietorship, or Type D or
"disregarded entity;" a partnership, or Type P; or a corporation, Type
C.
Sole Proprietorships and Partnerships
If your payee is an LLC that is taxed as a sole proprietorship,
you must issue the 1099 with certain information needed by the IRS. This
includes the name of the sole proprietor, the name of the LLC and the
Social Security number of the sole proprietor, which serves him as the
tax identification number. If the LLC is taxed as a partnership, then
the 1099 must carry the name of the business as well as its employer
identification number, or EIN.
Corporations
You do not need to issue the 1099 to an LLC that is classified as a
corporation for federal tax purposes. Corporations have strict IRS
guidelines and different forms for reporting income that replace the use
of a 1099. You may issue the 1099 to a corporation if you wish, but the
purpose would only be to simplify your own recordkeeping. You also do
not need to issue a 1099 to any LLC structure when you pay transaction
costs for merchandise including the item cost, postage charges, delivery
costs and storage.
