What is the name of this symbol "♪"?

The ♪ symbol is called a quaver, it represents 1/8th of the total duration represented by a full note

The one that looks similar to ♪, but doesn't have the little thingy sticking out and is not coloured inside is called a minim and is half of a full note

PS: if I understand it correctly, the "common name" above refers to what they are known as in the US. The traditional names for the notes are the ones in the Classical Note Name and are also more frequently used in music books

EDIT My answer has the most upvotes (as I type this). However I now believe that the answer provided by user13267 is better. I also think that the answer by Drew adds useful information.

In the US, the answer is as given by the user lightbulb.

In the UK we have individual names for them. ♪ is a quaver, ♩ is a crotchet. Then we have minim, semibreve and breve.

Note that I have answered your query about the names of symbols. If you have queries about the meaning and execution of the symbols you will find the Music Stack Exchange very useful.

The Unicode character you used, ♪, is named EIGHTH NOTE. (Its Unicode code point is 9834 decimal, 266A hexadecimal.)

The "d"-like character ♩ is named QUARTER NOTE. (Its code point is 9833 decimal, 2669 hexadecimal.)

This, empty-"d" character, 𝅗𝅥, is named MUSICAL SYMBOL HALF NOTE. (Its code point is 119134 decimal, 1D15E hexadecimal.) But it does not show properly in the font used here.

See this for more about Unicode musical note symbols (characters).

Those symbols are examples of musical notes.

In American English:

♪ is an eighth note. ♩ is a quarter note. The other symbols are "half" and "whole" notes respectively. Their names reflect the notes' durations as a fraction of a measure in 4/4 time.