Even as a single member LLC you must keep finances separate. You must have a bank account for the LLC which is not your personal bank account. Then you can pay yourself (or take dividends) from the LLC funds. But you can not deposit the LLC money into a personal bank account. Well, you aren't supposed to. I guess a bank may allow you to, but legally you really want separate accounts.
There is a legal difference between you and the LLC. You need to financially operate as if you are not the LLC and the LLC is not you. And you need to present the business as an LLC not as you personally. It's fine if you present the business as an LLC owned and operated by yourself. But you should never get payments from clients under your personal name. They should all be paying the LLC, not you. (To be frank, any client worried about this is probably not worth the gas it takes to drive to the bank to deposit their check. I've never, in over a decade, run into a single client that had a problem making a check payable to my LLC rather than to me.)
You should never be paying for personal items (groceries, dates, entertainment, etc) from the LLC account. The LLC account should only be paying business expenses. It is also wise to not pay yourself a regular, steady paycheck from the LLC. You can take dividends whenever you want, but not adhering to a set schedule is beneficial (at least that's what I was advised by my attorney). So take some this week/month, then don't take anything a couple weeks/month, then take a different amount the following week/month ... that sort of thing.
The entire point of an LLC is to "Limit" your "Liability". If you fail to keep finances separate, and appear to be "living" off the LLC, a judge can immediately dissolve a single member LLC and hold you personally responsible for any judgement/settlement (heaven forbid) rather than the LLC, thus removing all liability limits. As a single member LLC, only by rigidly keeping finances separate can you try to combat such an occurrence.
All that being posted.....
Yes, the IRS permits you to file taxes as an "individual with a single-member LLC" rather than filing twice. You won't be taxed twice. I run a single-member LLC and merely file a 1040 and schedule C every year under my name, not my LLC. The income is added to your taxes as 1099 income or "general" income along with any W2 income. You do not file taxes for the LLC... you file your personal taxes claiming the money earned through the LLC. This option of filing taxes on you own, personal taxes is only permitted by single-member LLCs or sole proprietorships. As soon as you have another member in the LLC.... then the LLC will need to file its own taxes. And at that point I'd suggest you hire an accountant if you haven't done so already, because then you get into tax issues with payouts to members (dividends), etc. and things are no long "easy" at that point.
(Yes, basically the IRS treats the LLC as if you are the LLC ... but a judge doesn't want you to to that if you wish to actually limit any liability. That's government for you.)