I'm new to D&D and I'm building a Beast Master ranger. Is there a full list of companions that I can use? That way, I know which ones are at my disposal.
Rangers can only choose a beast type monster that is no larger than Medium in size and has a Challenge Rating of 1/4 or lower. Page 317, Appendix A of the Monster Manual covers at least 90% of the beasts that have been statted for 5e. Although it's not a comprehensive list of the Ranger's animal companion options, it's really not that hard to sort out what you can and can't use.
Some of these beasts are also covered starting on page 304, Appendix D, of the PHB.
WoTC has also created a PDF of monsters by type. Again, it's not a list tailored for the Ranger's companions but it does list all the beasts and their Challenge Ratings so you should be able to work it out from there.
With the release of Volo's Guide to Monsters there is also a 'monsters by type' list on page 221 that has additional beasts that were added in that book.
And as BlueMoon has already pointed out, dndbeyond has the ability to filter monsters by type, size, CR, etc. and that will give you an even more comprehensive list of available beasts that also includes those from official adventure modules. It should, however, be noted that you do need to have purchased the material on dndbeyond should you wish to have access to the stat blocks of the creatures not covered by the Basic Rules.
D&D Beyond has such a list.
If you filter the monsters in D&D Beyond, you will have ALL the possible animal companions you can have (I don't think you can filter out swarms, but all others are fair game).
The list has all their stats, source-books, etc. It is exceedingly useful for me, and is unlikely to disappear.