As a single member LLC, you would normally use your social security number. Since you've formed a S-corp with form 2553, you'll now enter your s-corporation name, which is your LLC name (as used on form 2553), on line 1 of the W-9.
In box 3 of the W-9, you should select the 6th checkbox for Limited Liability Company and enter "S" for S-corporation, in the space to the right. Now that your business name is an s-corp, it is not a disregarded entity by the IRS, it's a s-corporation.
To see this information at the IRS see page 3 of the instructions here: https://www.irs.gov/pub/irs-pdf/fw9.pdf