In order to do that, your LLC has to elect to be taxed as an S-corp, which requires it to file its own return. Worse, certain states and cities will impose a corporation tax on it.
Otherwise, if you retain disregarded entity status, you have to use your personal SSN for invoices. The corporation EIN is then mostly for employment tax purposes.
(Not actual tax advice)
"For example, if a disregarded entity LLC that is owned by an individual is required to provide a Form W-9, Request for Taxpayer Identification Number (TIN) and Certification, the W-9 should provide the owner’s SSN or EIN, not the LLC’s EIN." [0]
[0] https://www.irs.gov/businesses/small-businesses-self-employe...