Spoilers
- David Tennant regenerated in front of Rose, and then visited her before succumbing to radiation in the TARDIS.
- Matt Smith crash landed in Amelia Pond's garden and also hallucinated her saying goodbye to him before he regenerated ("...the first face this face saw").
- Christopher Eccleston regenerated alone in the TARDIS, and as of September 2015 his first moments have not been revealed, but certain scenes in Doctor Who: Rose (2005) (such as him studying himself in Rose's mirror), imply that he was new to his body. At the very least this confirms that Rose was his first (and only) companion, possibly the first person he ever spoke to.
The only Doctor this does not apply to is the War Doctor, who regenerated from Paul McGann's Eighth Doctor in front of the Sisterhood of Karn ( Doctor Who: The Night of the Doctor (2013) ) but regenerated alone in his TARDIS after the events of Doctor Who: The Day of the Doctor (2013). In fact, the last people he saw before changing were the Tenth and Eleventh incarnations of his future self (and Clara).