Jelly, 20 bytes

œṡ⁶Ṛj⁾, ;“Œ1~»“Hi ”;

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A monadic link taking the input as its argument and returning a Jelly string.

Explanation

œṡ⁶ | Split at first space
 Ṛ | Reverse
 j⁾, | Join with ", "
 ;“Œ1~» | Concatenate " Jelly!" to the end
 “Hi ”; | Concatenate "Hi " to the beginning

Ruby -p, 32 28 bytes

-4 bytes by leveraging Nick Kennedy's Jelly answer.

~/ /;$_="Hi #$', I'm Ruby!"

Explanation

 # -p gets line of input and saves to $_
~/ /; # Find first space in $_ using regex
 $_="Hi #$', I'm Ruby!" # Save modified string to $_
 # ($' is the string AFTER the most recent regex match)
 # -p outputs $_ to screen

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brainfuck, 164

,-.+>,>,----.++++>,.>,[.,]<<<+++++.----->>.[<]>[.>]<[->+++<]>++.[--->+<]>----.+++[->+++<]>++.++++++++.+++++.--------.-[--->+<]>--.+[->+++<]>+.++++++++.+[++>---<]>-.

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The "brainfuck!" part of the string is generated with this tool, can probably be golfed further by hand.

J, 22 bytes

', I''m J!',~'Hi',3}.]

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Stax, 13 bytes

â∞¿φ‼0▲(─ƒSqÄ

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Octave, 35 bytes

@(s)["Hi" s(4:end) ", I'm Octave!"]

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@(s) % Anonymous function taking a string input
 [ ] % Concatenate everything inside the brackets
 "Hi" ", I'm Octave!"] % The fixed parts of the output string
 s(4:end) % The input, except "I'm"

 % Returns the concatenated string

42 bytes:

I tried retrieving "Octave" somehow, without writing it out, since 6 chars is quite a lot compared to some of the other language names here. Unfortunately, I could only find ver, which outputs a struct with comma separated fields. Takes way more than 6 bytes. :(

@(s)["Hi" s(4:end) ", I'm " ver.Name1]

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Japt, 18 bytes

`His3, I'm Japt!

When Japt's string compression library achieves a 0% compress rate...

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APL+WIN, 31 bytes

s," ",("Hi",3↓s←⎕),", I'm APL!"

Prompts for input string.

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One byte extra in TIO as Dyalog Classic requires quotes within text strings to be doubled up whereas double quotes can be used to enclose text strings in APL+WIN.

Perl 6, 30 28 bytes

-2 bytes thanks to bb94

"Him/s.*/, I'm Perl 6!"

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JavaScript, 38 37 bytes

x=>`Hi$x.slice(3), I'm JavaScript!`

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Python 3, 35 bytes

lambda s:"Hi"+s[3:]+", I'm Python!"

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C# (Visual C# Interactive Compiler), 33 bytes

n=>$"Hin.Substring(3), I'm C#!"

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C (gcc), 59 42 bytes

-17 bytes thanks to @Conor O'Brien noticing that the import wasn't necessary

int a(char*x)printf("Hi%s, I'm C!",x+3);

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Chops off the first 3 characters of the input (removes I'm) and surrounds it with the desired text

Perl 5 -p, 31 bytes

s/I'm/Hi/;$=", I'm Perl 5 -p!"

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05AB1E, 23 bytes

#À„Hiš`s',«s"05AB1E!"ðý

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Explanation

# # split on spaces
 À # rotate left
 „Hiš # prepend "Hi"
 ` # split as separate words to the stack
 s # move the adjective to the top of the stack
 ',« # append ","
 s # swap "I'm" to the top of the stack
 "05AB1E!" # push the language name
 ðý # join on spaces

V, 15 bytes

c3lHi␛A, I'm V!

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New to V. Just knew it about 30 minutes ago. Anyway, this language is chosen just because its name only cost 1 byte. I'm not sure how to send <End> key in V. Most vim environment would accept <End> as a replacement of <Esc>A in this example. But, you know, V is 2 characters shorter than vim. :)